Skip to main content

Showing 1–200 of 507 results for report_num: CPH-SYM

.
  1. arXiv:2110.03437  [pdf, ps, other

    math.QA math.OA

    Symmetry Reduction of States II: A non-commutative Positivstellensatz for CPn

    Authors: Philipp Schmitt, Matthias Schötz

    Abstract: We give a non-commutative Positivstellensatz for CP^n: The (commutative) *-algebra of polynomials on the real algebraic set CP^n with the pointwise product can be realized by phase space reduction as the U(1)-invariant polynomials on C^{1+n}, restricted to the real (2n+1)-sphere inside C^{1+n}, and Schmüdgen's Positivstellensatz gives an algebraic description of the real-valued U(1)-invariant poly… ▽ More

    Submitted 18 January, 2022; v1 submitted 5 October, 2021; originally announced October 2021.

    Comments: 24 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L65 (Primary); 14P99 (Secondary)

  2. arXiv:2108.02473  [pdf, other

    math.CT math.AG math.AT math.QA math.SG

    The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory

    Authors: Damien Calaque, Rune Haugseng, Claudia Scheimbauer

    Abstract: We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological version of the classical AKSZ field theories that occur in physics. These have as their targets higher categories of symplectic derived stacks, with higher morphisms given by iterated Lagrangian correspondences. We defi… ▽ More

    Submitted 16 November, 2022; v1 submitted 5 August, 2021; originally announced August 2021.

    Comments: Minor revs. Final version. 175 pages. Some refs have been updated. To appear in Memoirs of the AMS

    Report number: CPH-SYM-DNRF92

  3. arXiv:2108.01924  [pdf, ps, other

    math.KT

    The reductive Borel-Serre compactification as a model for unstable algebraic K-theory

    Authors: Dustin Clausen, Mikala Ørsnes Jansen

    Abstract: Let $A$ be an associative ring and $M$ a finitely generated projective $A$-module. We introduce a category $\operatorname{RBS}(M)$ and prove several theorems which show that its geometric realisation functions as a well-behaved unstable algebraic K-theory space. These categories $\operatorname{RBS}(M)$ naturally arise as generalisations of the exit path $\infty$-category of the reductive Borel-Ser… ▽ More

    Submitted 21 November, 2023; v1 submitted 4 August, 2021; originally announced August 2021.

    Comments: 89 pages; v2 minor revision; v3 final accepted version, minor errors fixed, to appear in Selecta Mathematica

    Report number: CPH-GEOTOP-DNRF151, CPH-SYM-DNRF92

  4. The stratified homotopy type of the reductive Borel-Serre compactification

    Authors: Mikala Ørsnes Jansen

    Abstract: We identify the exit path $\infty$-category of the reductive Borel-Serre compactification as the nerve of a $1$-category defined purely in terms of rational parabolic subgroups and their unipotent radicals. As an immediate consequence, we identify the fundamental group of the reductive Borel-Serre compactification, recovering a result of Ji-Murty-Saper-Scherk, and we obtain a combinatorial incarna… ▽ More

    Submitted 4 January, 2023; v1 submitted 19 December, 2020; originally announced December 2020.

    Comments: 47 pages, 1 figure, v2: minor revision, v3: final accepted version, some typos corrected

    Report number: CPH-GEOTOP-DNRF151, CPH-SYM-DNRF92

    Journal ref: International Mathematics Research Notices, 2022

  5. arXiv:2009.11620  [pdf, ps, other

    math.RT math.AT

    Decompositions of the stable module $\infty$-category

    Authors: Joshua Hunt

    Abstract: We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgrou… ▽ More

    Submitted 24 September, 2020; originally announced September 2020.

    Comments: 16 pages

    Report number: CPH-SYM-DNRF92,CPH-GEOTOP-DNRF151

  6. arXiv:2008.09906  [pdf, ps, other

    math.AT math.CT

    Homotopy characters as a homotopy limit

    Authors: Sergey Arkhipov, Daria Poliakova

    Abstract: For a Hopf DG-algebra corresponding to a derived algebraic group, we compute the homotopy limit of the associated cosimplicial system of DG-algebras given by the classifying space construction. The homotopy limit is taken in the model category of DG-categories. The objects of the resulting DG-category are Maurer-Cartan elements of $\operatorname{Cobar}(A)$, or 1-dimensional $A_\infty$-comodules ov… ▽ More

    Submitted 22 August, 2020; originally announced August 2020.

    Comments: 21 pages, no figures

    Report number: CPH-SYM-DNRF92 MSC Class: 18G35 (Primary); 18G80; 55U35 (Secondary)

  7. Torsion Free Endotrivial Modules for Finite Groups of Lie Type

    Authors: Jon F. Carlson, Jesper Grodal, Nadia Mazza, Daniel K. Nakano

    Abstract: In this paper we determine the torsion free rank of the group of endotrivial modules for any finite group of Lie type, in both defining and non-defining characteristic. On our way to proving this, we classify the maximal rank $2$ elementary abelian $\ell$-subgroups in any finite group of Lie type, for any prime $\ell$, which may be of independent interest.

    Submitted 24 June, 2021; v1 submitted 1 May, 2020; originally announced May 2020.

    Report number: CPH-SYM-DNRF92, CPH-GEOTOP-DNRF151 MSC Class: 20C33;

    Journal ref: Pacific J. Math. 317 (2022) 239-274

  8. arXiv:2004.06889  [pdf, ps, other

    math.AT math.GT math.KT

    On the homotopy type of L-spectra of the integers

    Authors: Fabian Hebestreit, Markus Land, Thomas Nikolaus

    Abstract: We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and a generalised Eilenberg-Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L-spectra recently devised for the study of Grothen… ▽ More

    Submitted 25 May, 2021; v1 submitted 15 April, 2020; originally announced April 2020.

    Comments: v3: Removed an erroneous (but for the paper irrelevant) remark in the appendix. An erratum is available from the webpages of the authors

    Report number: CPH-SYM-DNRF92

  9. arXiv:2003.07852  [pdf, other

    math.AT math.GR math.RT

    String topology of finite groups of Lie type

    Authors: Jesper Grodal, Anssi Lahtinen

    Abstract: We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the corresponding compact Lie group $G$, via ring and module structures constructed from string topology, a la Chas-Sullivan. If a certain fundamental class in the h… ▽ More

    Submitted 17 March, 2020; originally announced March 2020.

    Comments: 58 pages

    Report number: CPH-SYM-DNRF92, CPH-GEOTOP-DNRF151 MSC Class: 20J06 (Primary) 20D06; 55R35; 55P50 (Secondary)

  10. arXiv:2001.02781  [pdf, ps, other

    math.AT

    Homology operations revisited

    Authors: Anssi Lahtinen

    Abstract: The mod p homology of E-infinity spaces is a classical topic in algebraic topology traditionally approached in terms of Dyer--Lashof operations. In this paper, we offer a new perspective on the subject by providing a detailed investigation of an alternative family of homology operations equivalent to, but distinct from, the Dyer--Lashof operations. Among other things, we will relate these operatio… ▽ More

    Submitted 8 January, 2020; originally announced January 2020.

    Comments: 47 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 55S99 (Primary) 55S15; 55P47 (Secondary)

  11. Local Gorenstein duality for cochains on spaces

    Authors: Tobias Barthel, Natalia Castellana, Drew Heard, Gabriel Valenzuela

    Abstract: We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein duality along morphisms of $k$-algebras. Our main examples are of the form $R = C^*(X;k)$, the ring spectrum of cochains on a space $X$ for a field $k$. In particul… ▽ More

    Submitted 21 July, 2020; v1 submitted 8 January, 2020; originally announced January 2020.

    Comments: 21 pages, comments welcome. v2 ,version to appear (with minor formatting differences) in Journal of Pure and Applied Algebra

    Report number: CPH-SYM-DNRF92

  12. arXiv:1912.10239  [pdf, ps, other

    math.AT math.GT

    Operations on stable moduli spaces

    Authors: Soren Galatius, Oscar Randal-Williams

    Abstract: We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in a stable range provided the $p$-adic valuation of the Euler characteristics agree, for all primes $p$ not invertible in the coefficients for cohomology.

    Submitted 22 March, 2020; v1 submitted 21 December, 2019; originally announced December 2019.

    Comments: 12 pages. Based on excised section of arXiv:1601.00232v1. Final accepted version

    Report number: CPH-SYM-DNRF92 MSC Class: 57R90; 57R15; 57R56; 55P47

  13. arXiv:1912.08970  [pdf, ps, other

    math.AG math.KT

    Descent for semiorthogonal decompositions

    Authors: Benjamin Antieau, Elden Elmanto

    Abstract: We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not only admissible subcategories but also preferred objects.

    Submitted 9 January, 2021; v1 submitted 18 December, 2019; originally announced December 2019.

    Comments: Various minor changes, new example from Hodge theory; to appear in Advances in Mathematics

    Report number: CPH-SYM-DNRF92 MSC Class: 14F05; 14F22; 14M17; 18E30

  14. arXiv:1912.07583  [pdf, ps, other

    math.AT math.AG math.GT

    Global group laws and equivariant bordism rings

    Authors: Markus Hausmann

    Abstract: For every abelian compact Lie group A, we prove that the homotopical A-equivariant complex bordism ring, introduced by tom Dieck (1970), is isomorphic to the A-equivariant Lazard ring, introduced by Cole-Greenlees-Kriz (2000). This settles a conjecture of Greenlees. We also show an analog for homotopical real bordism rings over elementary abelian 2-groups. Our results generalize classical theorems… ▽ More

    Submitted 7 February, 2022; v1 submitted 16 December, 2019; originally announced December 2019.

    Comments: Final version to appear in Annals of Mathematics

    Report number: CPH-SYM-DNRF92

  15. arXiv:1912.05212  [pdf, ps, other

    math.OA math.DS

    Balanced strong shift equivalence, balanced in-splits, and eventual conjugacy

    Authors: Kevin Aguyar Brix

    Abstract: We introduce the notion of balanced strong shift equivalence between square nonnegative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate to balanced strong shift equivalent matrices. Moreover, we show that such graphs are eventually conjugate if and only if one can be reached by the other via a… ▽ More

    Submitted 9 December, 2020; v1 submitted 11 December, 2019; originally announced December 2019.

    Comments: Minor changes, examples have been distributed throughout the manuscript, 21 pages. This is the published version

    Report number: CPH-SYM-DNRF92

  16. Wick Rotations in Deformation Quantization

    Authors: Philipp Schmitt, Matthias Schötz

    Abstract: We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from $\mathbb{C}^{1+n}$ with the Wick star product in arbitrary signature. Two special cases of such manifolds are the complex projective space $\mathbb{CP}^n$ and the complex hyperbolic disc $\mathbb{D}^n$. We generalize several older results to this setting: The constru… ▽ More

    Submitted 31 January, 2020; v1 submitted 27 November, 2019; originally announced November 2019.

    Report number: CPH-SYM-DNRF92

  17. arXiv:1911.10423  [pdf, ps, other

    math.OA math.PR

    Doob equivalence and non-commutative peaking for Markov chains

    Authors: Xinxin Chen, Adam Dor-On, Langwen Hui, Christopher Linden, Yifan Zhang

    Abstract: In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional probabilities in terms of (generalized) Doob transforms, which then leads to a stronger classification result for the associated operator algebras in terms of spectral ra… ▽ More

    Submitted 23 November, 2019; originally announced November 2019.

    Comments: 14 pages. Comments welcome !

    Report number: CPH-SYM-DNRF92 MSC Class: Primary: 60J10; 47L80. Secondary: 60J45; 60J50; 47L75

  18. arXiv:1910.13562  [pdf, ps, other

    math.QA math.CT

    The Reduced Tensor Product of Braided Tensor Categories Containing a Symmetric Fusion Category

    Authors: Thomas A. Wasserman

    Abstract: We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The construction only depends on the braiding and monoidal structure of the categories involved. The main tool in the construction is an enriching procedure that is sho… ▽ More

    Submitted 29 October, 2019; originally announced October 2019.

    Comments: 42 pages, many diagrams

    Report number: CPH-SYM-DNRF92 MSC Class: 18D10

  19. arXiv:1910.13557  [pdf, ps, other

    math.QA math.CT

    Drinfeld Centre-Crossed Braided Tensor Categories

    Authors: Thomas A. Wasserman

    Abstract: We introduce, for a symmetric fusion category $\mathcal{A}$ with Drinfeld centre $\mathcal{Z}(\mathcal{A})$, the notion of $\mathcal{Z}(\mathcal{A})$-crossed braided tensor category. These are categories that are enriched over $\mathcal{Z}(\mathcal{A})$ equipped with a symmetric tensor product, while being braided monoidal with respect to the usual tensor product on $\mathcal{Z}(\mathcal{A})$. I… ▽ More

    Submitted 29 October, 2019; originally announced October 2019.

    Comments: 46 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 18D10

  20. arXiv:1910.11514  [pdf, ps, other

    math.OA

    Geometric classification of isomorphism of unital graph C*-algebras

    Authors: Sara E. Arklint, Søren Eilers, Efren Ruiz

    Abstract: We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and finitely or countably infinitely many edges, corresponding to unital and separable C*-algebras.

    Submitted 24 October, 2019; originally announced October 2019.

    Report number: CPH-SYM-DNRF92

  21. arXiv:1910.06504  [pdf, ps, other

    math.OA math.KT

    Classification of $\mathcal O_\infty$-stable $C^\ast$-algebras

    Authors: James Gabe

    Abstract: I present a proof of Kirchberg's classification theorem: two separable, nuclear, $\mathcal O_\infty$-stable $C^\ast$-algebras are stably isomorphic if and only if they are ideal-related $KK$-equivalent. In particular, this provides a more elementary proof of the Kirchberg--Phillips theorem which is isolated in the paper to increase readability of this important special case.

    Submitted 30 June, 2021; v1 submitted 14 October, 2019; originally announced October 2019.

    Comments: To appear in Mem. Amer. Math. Soc., 112 pages, v3 (accepted version): added two subsections (8.4 and 15.3) on approximate equivalence. v2: minor changes

    Report number: CPH-SYM-DNRF92 MSC Class: 46L35; 46L80

  22. arXiv:1910.06191  [pdf, ps, other

    math.AT

    Tate blueshift and vanishing for Real oriented cohomology

    Authors: Guchuan Li, Vitaly Lorman, J. D. Quigley

    Abstract: We study transchromatic phenomena for the Tate construction of Real oriented cohomology theories. First, we show that after suitable completion, the Tate construction with respect to a trivial $\mathbb{Z}/2$-action on height $n$ Real Johnson--Wilson theory splits into a wedge of height $n-1$ Real Johnson--Wilson theories. This is the first example of Tate blueshift at all chromatic heights outside… ▽ More

    Submitted 6 May, 2022; v1 submitted 14 October, 2019; originally announced October 2019.

    Comments: 38 pages. v2: Revised exposition and expanded some proofs. v3: Updated funding sources and bibliography. v4: Revised intro, clarified some arguments. Comments welcome!

    Report number: CPH-SYM-DNRF92 MSC Class: 55N25; 55P42; 55P60; 55P91; 55P92

  23. C*-algebras, groupoids and covers of shift spaces

    Authors: Kevin Aguyar Brix, Toke Meier Carlsen

    Abstract: To every one-sided shift space $\mathsf{X}$ we associate a cover $\tilde{\mathsf{X}}$, a groupoid $\mathcal{G}_{\mathsf{X}}$ and a $\mathrm{C^*}$-algebra $\mathcal{O}_{\mathsf{X}}$. We characterize one-sided conjugacy, eventual conjugacy and (stabilizer preserving) continuous orbit equivalence between $\mathsf{X}$ and $\mathsf{Y}$ in terms of isomorphism of $\mathcal{G}_{\mathsf{X}}$ and… ▽ More

    Submitted 21 November, 2020; v1 submitted 4 October, 2019; originally announced October 2019.

    Comments: 45 pages; Section 3 and Theorem 3.3 improved, other minor changes. This is the published version

    Report number: CPH-SYM-DNRF92

    Journal ref: Trans. Amer. Math. Soc. Ser. B 7 (2020), 134-185

  24. arXiv:1909.10042  [pdf, ps, other

    math.AT math.CT

    Algebras for enriched $\infty$-operads

    Authors: Rune Haugseng

    Abstract: Using the description of enriched $\infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $\infty$-operads as certain modules in symmetric sequences. For $\mathbf{V}$ a nice symmetric monoidal model category, we prove that strict algebras for $Σ$-cofibrant operads in $\mathbf{V}$ are equivalent to algebras in the associated symmetric monoidal $\infty$-categ… ▽ More

    Submitted 22 September, 2019; originally announced September 2019.

    Comments: 15 pages

    Report number: CPH-SYM-DNRF92

  25. arXiv:1908.03857  [pdf, other

    math.AT math.DG math.GT

    On the invariance of the string topology coproduct

    Authors: Nancy Hingston, Nathalie Wahl

    Abstract: We show that the Goresky-Hingston coproduct in string topology is invariant under homotopy equivalences that satisfy an additional assumption, either stated in terms the restriction to the ``fake diagonal'', or in terms of boundedness for the homotopy.

    Submitted 9 September, 2021; v1 submitted 11 August, 2019; originally announced August 2019.

    Comments: Mistake corrected, with added assumption to the main theorem

    Report number: CPH-SYM-DNRF92, CPH-GeoTop-DNRF151

  26. arXiv:1908.03714  [pdf, ps, other

    math.OA math.DS

    Refined moves for structure-preserving isomorphism of graph C*-algebras

    Authors: Søren Eilers, Efren Ruiz

    Abstract: We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose a list of seven types of moves that we conjecture has the property that the collection of moves respecting one of six notions of isomorphism indeed generate that notion, in the sense that two graphs a… ▽ More

    Submitted 10 August, 2019; originally announced August 2019.

    Report number: CPH-SYM-DNRF92

  27. arXiv:1908.01329  [pdf, ps, other

    math.OA

    A Groupoid Picture of Elek Algebras

    Authors: Clemens Borys

    Abstract: We describe a construction by Gábor Elek, associating C*-algebras with uniformly recurrent subgroups, in the language of groupoid C*-algebras. This allows us to simplify several proofs in the original paper and fully characterise their nuclearity. We furthermore relate our groupoids to the dynamics of the group acting on its uniformly recurrent subgroup.

    Submitted 4 August, 2019; originally announced August 2019.

    Comments: 11 pages

    Report number: CPH-SYM-DNRF92

  28. Proper equivariant stable homotopy theory

    Authors: Dieter Degrijse, Markus Hausmann, Wolfgang Lück, Irakli Patchkoria, Stefan Schwede

    Abstract: This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from equivariant cells with compact isotropy groups; the adjective `genuine' indicates that the theory comes with appropriate transfers and Wirthmüller isomorphisms… ▽ More

    Submitted 14 October, 2020; v1 submitted 2 August, 2019; originally announced August 2019.

    Comments: several minor corrections and updates; v+142 pp

    Report number: CPH-SYM-DNRF92 MSC Class: 55P91

    Journal ref: Memoirs of the American Mathematical Society 288 (2023), No. 1432

  29. arXiv:1907.03977  [pdf, other

    math.AT math.CT

    Homotopy-coherent algebra via Segal conditions

    Authors: Hongyi Chu, Rune Haugseng

    Abstract: Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", bywhich we mean an $\infty$-category equipped with a factorization system and a collection of "elementary" objects. Examples of structures that occur as such "Segal $\mathcal{O}$-spaces" for an algebraic pattern $\mathcal{O}$ include $\infty$-categories, $(\infty,n)$-ca… ▽ More

    Submitted 6 March, 2021; v1 submitted 9 July, 2019; originally announced July 2019.

    Comments: 66 pages, v2: Fixed a serious mistake in the relation between extendable patterns and polynomial monads, v3: Many small corrections and improvements

    Report number: CPH-SYM-DNRF92

  30. arXiv:1907.03185  [pdf, ps, other

    math.QA

    Strict quantization of coadjoint orbits

    Authors: Philipp Schmitt

    Abstract: We obtain a family of strict $\hat G$-invariant products on the space of holomorphic functions on a semisimple coadjoint orbit of a complex connected semisimple Lie group $\hat G$. By restriction, we also obtain strict $G$-invariant products $*_\hbar$ on a space $A(O)$ of certain analytic functions on a semisimple coadjoint orbit $O$ of a real connected semisimple Lie group $G$. The space $A(O)$ e… ▽ More

    Submitted 20 January, 2022; v1 submitted 6 July, 2019; originally announced July 2019.

    Comments: 54 pages. Comments are welcome!

    Report number: CPH-SYM-DNRF92 MSC Class: 53D55; 17B08; 32Q28; 22E46

  31. Classification of irreversible and reversible Pimsner operator algebras

    Authors: Adam Dor-On, Søren Eilers, Shirly Geffen

    Abstract: Since their inception in the 30's by von Neumann, operator algebras have been used in shedding light in many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two was sought since their emergence in the late 60's. We connect these seemingly separate type of results by uncovering a hiera… ▽ More

    Submitted 31 May, 2020; v1 submitted 2 July, 2019; originally announced July 2019.

    Comments: 1 figure, 28 pages. To appear in Compositio Mathematica

    Report number: CPH-SYM-DNRF92 MSC Class: Primary: 47L30; 46L35. Secondary: 47L55; 46L80; 46L08

    Journal ref: Compositio Math. 156 (2020) 2510-2535

  32. arXiv:1905.11637  [pdf, ps, other

    math.GT math.AT math.DS

    Dynamical and cohomological obstructions to extending group actions

    Authors: Kathryn Mann, Sam Nariman

    Abstract: We study cohomological obstructions to extending group actions on the boundary $\partial M$ of a $3$-manifold to a $C^0$-action on $M$ when $\partial M$ is diffeomorphic to a torus or a sphere. In particular, we show that for a $3$-manifold $M$ with torus boundary which is not diffeomorphic to a solid torus, the torus action on the boundary does not extend to a $C^0$-action on $M$.

    Submitted 28 December, 2020; v1 submitted 28 May, 2019; originally announced May 2019.

    Comments: Minor correction to statement of Theorem 1.3

    Report number: CPH-SYM-DNRF92 MSC Class: 57R50; 57R19; 57M60; 19J35; 55R40; 37C85

  33. arXiv:1905.05630  [pdf, ps, other

    math.OA math.FA math.GR math.QA

    The Hadamard product in a crossed product C*-algebra

    Authors: Erik Christensen

    Abstract: We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We show that this product has a natural Stinespring representation and we lift some known results on block Schur products to this setting, but we also show that… ▽ More

    Submitted 12 June, 2019; v1 submitted 14 May, 2019; originally announced May 2019.

    Comments: The Stinespring representation of the Hadamard product is now given in a simple explicit form

    Report number: CPH-SYM-DNRF92 MSC Class: 15A69; 22D15; 43A30; 46L05; 47L65; 81T05

  34. arXiv:1905.00872  [pdf, ps, other

    math.AG

    Functorial destackification and weak factorization of orbifolds

    Authors: Daniel Bergh, David Rydh

    Abstract: Let X be a smooth and tame stack with finite inertia. We prove that there is a functorial sequence of blow-ups with smooth centers after which the stabilizers of X become abelian. Using this result, we can extend the destackification results of the first author to any smooth tame stack. We give applications to resolution of tame quotient singularities, prime-to-l alterations of singularities and w… ▽ More

    Submitted 2 May, 2019; originally announced May 2019.

    Comments: 38 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 14A20; 14E15

  35. arXiv:1904.12841  [pdf, ps, other

    math.AT math.RT

    On stratification for spaces with Noetherian mod $p$ cohomology

    Authors: Tobias Barthel, Natalia Castellana, Drew Heard, Gabriel Valenzuela

    Abstract: Let $X$ be a topological space with Noetherian mod $p$ cohomology and let $C^*(X;\mathbb{F}_p)$ be the commutative ring spectrum of $\mathbb{F}_p$-valued cochains on $X$. The goal of this paper is to exhibit conditions under which the category of module spectra on $C^*(X;\mathbb{F}_p)$ is stratified in the sense of Benson, Iyengar, Krause, providing a classification of all its localizing subcatego… ▽ More

    Submitted 4 August, 2021; v1 submitted 29 April, 2019; originally announced April 2019.

    Comments: All comments welcome. v2 - version accepted for publication in the American Journal of Mathematics

    Report number: CPH-SYM-DNRF92

  36. arXiv:1904.11312  [pdf, ps, other

    math.AG math.AT math.CT math.SG

    Shifted Coisotropic Correspondences

    Authors: Rune Haugseng, Valerio Melani, Pavel Safronov

    Abstract: We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the $i$-morphisms are given by $i$-fold coisotropic correspondences. Assuming an expected equivalence of different models of higher Morita categories, we prove that all derived Poisson stacks are fully dualizable, and so determine frame… ▽ More

    Submitted 31 October, 2020; v1 submitted 25 April, 2019; originally announced April 2019.

    Comments: 51 pages, v2: accepted version

    Report number: CPH-SYM-DNRF92

  37. arXiv:1904.10062  [pdf, ps, other

    math.OA

    The Furstenberg Boundary of a Groupoid

    Authors: Clemens Borys

    Abstract: We define the Furstenberg boundary of a locally compact Hausdorff étale groupoid, generalising the Furstenberg boundary for discrete groups, by providing a construction of a groupoid-equivariant injective envelope. Using this injective envelope, we establish the absence of recurrent amenable subgroups in the isotropy as a sufficient criterion for the intersection property of a locally compact Haus… ▽ More

    Submitted 30 January, 2020; v1 submitted 22 April, 2019; originally announced April 2019.

    Comments: 20 pages, last section on applications to C*-simplicity added to previous version

    Report number: CPH-SYM-DNRF92

  38. arXiv:1904.08313  [pdf, ps, other

    math.GR math.LO math.OA

    A short proof of Thoma's theorem on type I groups

    Authors: Fabio Elio Tonti, Asger Törnquist

    Abstract: In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the irreducible unitary representations are what descriptive set theorists now call "concretely classifiable". Elmar Thoma [Tho64] proved the following surprising characteriz… ▽ More

    Submitted 16 April, 2019; originally announced April 2019.

    Comments: The statement of Lemma 7 has the following correction over earlier circulated drafts of the paper: The unnecessary assumption that H_0 and H_1 are non-abelian has been removed

    Report number: CPH-SYM-DNRF92

  39. The Ramsey property implies no mad families

    Authors: David Schrittesser, Asger Törnquist

    Abstract: We show that if all collections of infinite subsets of $\N$ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing problem going back to Mathias \cite{mathias}. The proof exploits an idea which has its natural roots in ergodic theory, topological dynamics, and invariant descriptive set theory: We use that a certain function associat… ▽ More

    Submitted 15 April, 2019; v1 submitted 11 April, 2019; originally announced April 2019.

    Comments: 10 pages; fixed a mistake in Theorem 4.4

    Report number: CPH-SYM-DNRF92 MSC Class: 03E05; 03E15; 03E25; 03E35; 03E60

    Journal ref: PNAS 116 (38) 18883--18887 (2019)

  40. arXiv:1904.05823  [pdf, ps, other

    math.LO

    Good projective witnesses

    Authors: Vera Fischer, Sy David Friedman, David Schrittesser, Asger Törnquist

    Abstract: We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality $\mathfrak a_{\text{g}}$ of a maximal cofinitary group (MCG) is strictly between $\aleph_1$ and $\mathfrak{c}$, and there is a $Π^1_2$-definable MCG of this cardinality. Here $Π^1_2$ is optimal, making this result a natural counterpart to the Borel MCG of… ▽ More

    Submitted 7 October, 2022; v1 submitted 11 April, 2019; originally announced April 2019.

    Comments: The exposition has been thoroughly revised; 33 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 03E17; 03E35

  41. arXiv:1903.10182  [pdf, ps, other

    math.OA

    Factorizable maps and traces on the universal free product of matrix algebras

    Authors: Magdalena Musat, Mikael Rørdam

    Abstract: We relate factorizable quantum channels on $M_n$, for $n \ge 2$, via their Choi matrix, to certain correlation matrices, which, in turn, are shown to be parametrized by traces on the unital free product $M_n * M_n$. Factorizable maps that admit a finite dimensional ancilla are parametrized by finite dimensional traces on $M_n * M_n$, and factorizable maps that approximately factor through finite d… ▽ More

    Submitted 17 October, 2019; v1 submitted 25 March, 2019; originally announced March 2019.

    Comments: 15 pages. To appear in Int. Math. Res. Not. IMRN

    Report number: CPH-SYM-DNRF92 MSC Class: 46L10; 81P45; 47L90

  42. Monochromatic homotopy theory is asymptotically algebraic

    Authors: Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton

    Abstract: In previous work, we used an $\infty$-categorical version of ultraproducts to show that, for a fixed height $n$, the symmetric monoidal $\infty$-categories of $E_{n,p}$-local spectra are asymptotically algebraic in the prime $p$. In this paper, we prove the analogous result for the symmetric monoidal $\infty$-categories of $K_{p}(n)$-local spectra, where $K_{p}(n)$ is Morava $K$-theory at height… ▽ More

    Submitted 24 March, 2019; originally announced March 2019.

    Comments: 33 pages

    Report number: CPH-SYM-DNRF92

  43. arXiv:1903.03818  [pdf, other

    math.GR

    Euler characteristics and p-singular elements in finite groups

    Authors: Jesper M. Møller

    Abstract: We use the Euler characteristic of the orbit category of a finite group to establish equivalences between theorems of Frobenius and K.S. Brown and between theorems of Steinberg and L. Solomon.

    Submitted 9 March, 2019; originally announced March 2019.

    Comments: 7 pages

    Report number: CPH-SYM-DNRF92

  44. arXiv:1902.05046  [pdf, ps, other

    math.AT

    A short introduction to the telescope and chromatic splitting conjectures

    Authors: Tobias Barthel

    Abstract: In this note, we give a brief overview of the telescope conjecture and the chromatic splitting conjecture in stable homotopy theory. In particular, we provide a proof of the folklore result that Ravenel's telescope conjecture for all heights combined is equivalent to the generalized telescope conjecture for the stable homotopy category, and explain some similarities with modular representation the… ▽ More

    Submitted 16 February, 2019; v1 submitted 13 February, 2019; originally announced February 2019.

    Comments: Accepted for publication in Surveys around Ohkawa's theorem on Bousfield classes. All comments welcome. v2: Corrected some typos

    Report number: CPH-SYM-DNRF92

  45. arXiv:1901.09004  [pdf, other

    math.AT

    Chromatic structures in stable homotopy theory

    Authors: Tobias Barthel, Agnès Beaudry

    Abstract: In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent developments in the field. Along the way, we illustrate the key methods and results with explicit examples.

    Submitted 29 April, 2019; v1 submitted 25 January, 2019; originally announced January 2019.

    Comments: To appear in the Handbook of Homotopy Theory. All comments welcome

    Report number: CPH-SYM-DNRF92

  46. arXiv:1901.08945  [pdf, ps, other

    math.AG

    Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties

    Authors: Daniel Bergh, Olaf M. Schnürer

    Abstract: It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of complexes of sheaves with quasi-coherent cohomology. This generalizes earlier work by Lieblich for gerbes over schemes whereas our gerbes may live over arbitrar… ▽ More

    Submitted 19 February, 2019; v1 submitted 25 January, 2019; originally announced January 2019.

    Comments: 28 pages. Comments are welcome. v2: Minor improvements of some proofs

    Report number: CPH-SYM-DNRF92 MSC Class: 14F05; 14A20

  47. arXiv:1812.08742  [pdf, other

    math.AT math.KT

    Homological stability for classical groups

    Authors: David Sprehn, Nathalie Wahl

    Abstract: We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite fields. Our result more generally applies to the automorphism groups of vector spaces equipped with a possibly degenerate form (in the sense of Bak, Tits and Wall). F… ▽ More

    Submitted 7 August, 2019; v1 submitted 20 December, 2018; originally announced December 2018.

    Comments: v2: Revision. Now recovers the Galatius-Kupers-Randal-Williams improved stability range for general linear groups over finite fields

    Report number: CPH-SYM-DNRF92

    Journal ref: Trans. Amer. Math. Soc. 373 (2020), 4807-4861

  48. arXiv:1812.07936  [pdf, ps, other

    math.NT math.AG

    Semistable abelian varieties and maximal torsion 1-crystalline submodules

    Authors: Cody Gunton

    Abstract: Let $p$ be a prime, let $K$ be a discretely valued extension of $\mathbb{Q}_p$, and let $A_{K}$ be an abelian $K$-variety with semistable reduction. Extending work by Kim and Marshall from the case where $p>2$ and $K/\mathbb{Q}_p$ is unramified, we prove an $l=p$ complement of a Galois cohomological formula of Grothendieck for the $l$-primary part of the Néron component group of $A_{K}$. Our proof… ▽ More

    Submitted 29 August, 2021; v1 submitted 19 December, 2018; originally announced December 2018.

    Comments: Final version

    Report number: CPH-SYM-DNRF92

    Journal ref: Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 39-81

  49. arXiv:1812.07506  [pdf, ps, other

    math.AG math.KT

    Perfection in motivic homotopy theory

    Authors: Elden Elmanto, Adeel A. Khan

    Abstract: We prove a topological invariance statement for the Morel-Voevodsky motivic homotopy category, up to inverting exponential characteristics of residue fields. This implies in particular that SH[1/p] of characteristic p>0 schemes is invariant under passing to perfections. Among other applications we prove Grothendieck-Verdier duality in this context.

    Submitted 19 June, 2019; v1 submitted 18 December, 2018; originally announced December 2018.

    Comments: 10 pages. v3: minor revisions; to appear in Proceedings of the LMS

    Report number: CPH-SYM-DNRF92

    Journal ref: Proc. Lond. Math. Soc. 120 (2020), no. 1, 28-38

  50. arXiv:1812.04555  [pdf, ps, other

    math.OA math.DS math.RT

    Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representations

    Authors: Mike Boyle, Benjamin Steinberg

    Abstract: We note that the deep results of Grunewald and Segal on algorithmic problems for arithmetic groups imply the decidability of several matrix equivalence problems involving poset-blocked matrices over Z. Consequently, results of Eilers, Restorff, Ruiz and Sørensen imply that isomorphism and stable isomorphism of unital graph C*-algebras (including the Cuntz-Krieger algebras) are decidable. One can a… ▽ More

    Submitted 30 May, 2020; v1 submitted 11 December, 2018; originally announced December 2018.

    Comments: 12 pages. This version (2) to appear in Proceedings AMS

    Report number: CPH-SYM-DNRF92 MSC Class: Primary 46L35; Secondary 16G20; 37B10

  51. arXiv:1812.03932  [pdf, ps, other

    math.AT math.CT

    A note on a Holstein construction

    Authors: Sergey Arkhipov, Daria Poliakova

    Abstract: We clarify details and fill certain gaps in the construction of a canonical Reedy fibrant resolution for a constant simplicial DG-category due to Holstein.

    Submitted 7 February, 2021; v1 submitted 10 December, 2018; originally announced December 2018.

    Comments: 12 pages, no figures; revised argument in Appendix A; Appendix B (Erratum) added

    Report number: CPH-SYM-DNRF92

    Journal ref: Homology, Homotopy and Applications, Vol. 22, No. 2, 04.2020, p. 151-162

  52. arXiv:1811.12219  [pdf, ps, other

    math.KT math.AT

    Forms over fields and Witt's lemma

    Authors: David Sprehn, Nathalie Wahl

    Abstract: We give an overview of the general framework of forms of Bak, Tits and Wall, when restricting to vector spaces over fields, and describe its relationship to the classical notions of Hermitian, alternating and quadratic forms. We then prove a version of Witt's lemma in this context, showing in particular that the action of the group of isometries of a space equipped with a form is transitive on iso… ▽ More

    Submitted 3 July, 2019; v1 submitted 29 November, 2018; originally announced November 2018.

    Comments: Final version, to appear in Math. Scand

    Report number: CPH-SYM-DNRF92

    Journal ref: Math. Scand. 126 (2020), 401-423

  53. arXiv:1811.04030  [pdf, ps, other

    math.AT

    A Whitehead theorem for periodic homotopy groups

    Authors: Tobias Barthel, Gijs Heuts, Lennart Meier

    Abstract: We show that $v_n$-periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.

    Submitted 17 July, 2019; v1 submitted 9 November, 2018; originally announced November 2018.

    Report number: CPH-SYM-DNRF92

  54. arXiv:1811.03668  [pdf, ps, other

    math.OA math-ph math.FA math.QA math.RT

    Decompositions of Schur block products

    Authors: Erik Christensen

    Abstract: Given two m x n matrices A = (a_{ij}) and B=(b_{ij}) with entries in B(H), the Schur block product is the m x n matrix A \square B := (a_{ij}b_{ij}). There exists an m x n contraction matrix S = (s_{ij}), such that A \square B = diag(AA*)^(1/2) S diag(B*B)^(1/2). This decomposition is also valid for the block Schur tensor product. It is shown, via the theory of random matrices, that the set of con… ▽ More

    Submitted 8 November, 2019; v1 submitted 8 November, 2018; originally announced November 2018.

    Comments: Nov. 2019, version accepted for publication. Some improvements based on the referee's comments

    Report number: CPH-SYM-DNRF92 MSC Class: 15A69; 46L07; 81P68; 46N50; 47L25; 81T05

  55. The extension problem for graph $C^*$-algebras

    Authors: Søren Eilers, James Gabe, Takeshi Katsura, Efren Ruiz, Mark Tomforde

    Abstract: We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.

    Submitted 6 July, 2020; v1 submitted 29 October, 2018; originally announced October 2018.

    Comments: Accepted version, to appear in Annals of K-theory

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55

    Journal ref: Ann. K-Th. 5 (2020) 295-315

  56. The unital Ext-groups and classification of $C^\ast$-algebras

    Authors: James Gabe, Efren Ruiz

    Abstract: The semigroups of unital extensions of separable $C^\ast$-algebras come in two flavours: a strong and a weak version. By the unital $\mathrm{Ext}$-groups, we mean the groups of invertible elements in these semigroups. We use the unital $\mathrm{Ext}$-groups to obtain $K$-theoretic classification of both unital and non-unital extensions of $C^\ast$-algebras, and in particular we obtain a complete… ▽ More

    Submitted 13 March, 2019; v1 submitted 25 October, 2018; originally announced October 2018.

    Comments: 31 pages. V2: Minor changes. To appear in Glasgow Math. J

    Report number: CPH-SYM-DNRF92 MSC Class: 46L35

  57. arXiv:1810.10848  [pdf, ps, other

    math.AG math.SG

    Weak $E_2$-Morita equivalences via quantization of the 1-shifted cotangent bundle

    Authors: Marton Hablicsek

    Abstract: In this paper, we investigate the structure of the convergent quantization of the 1-shifted cotangent bundle $S$ of a smooth scheme $X$ over a perfect field of positive characteristic. The quantization is an $E_2$-algebra over the Frobenius twist $S'$ of the 1-shifted cotangent bundle which restricted to the zero section $X'\rightarrow S'$ is weakly $E_2$-Morita equivalent to the structure sheaf… ▽ More

    Submitted 30 March, 2021; v1 submitted 25 October, 2018; originally announced October 2018.

    Report number: CPH-SYM-DNRF92

  58. arXiv:1810.06651  [pdf, ps, other

    math.AT

    Constructing the determinant sphere using a Tate twist

    Authors: Tobias Barthel, Agnès Beaudry, Paul G. Goerss, Vesna Stojanoska

    Abstract: Following an idea of Hopkins, we construct a model of the determinant sphere $S\langle det \rangle$ in the category of $K(n)$-local spectra. To do this, we build a spectrum which we call the Tate sphere $S(1)$. This is a $p$-complete sphere with a natural continuous action of $\mathbb{Z}_p^\times$. The Tate sphere inherits an action of $\mathbb{G}_n$ via the determinant and smashing Morava $E$-the… ▽ More

    Submitted 13 September, 2021; v1 submitted 15 October, 2018; originally announced October 2018.

    Comments: Revised version, including a correction and a newly included example in the last section

    Report number: CPH-SYM-DNRF92 MSC Class: 55P42; 55P92; 55P91; 55Q51

  59. arXiv:1810.05277  [pdf, ps, other

    math.AT math.GT

    The homotopy type of the topological cobordism category

    Authors: Mauricio Gomez-Lopez, Alexander Kupers

    Abstract: We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $Ω^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle over $BTop(d)$. We also give versions with tangential structures and boundary. The proof uses smoothing theory and excision in the tangential structure to reduce the… ▽ More

    Submitted 17 November, 2022; v1 submitted 11 October, 2018; originally announced October 2018.

    Comments: 56 pages, 9 figures. Final version

    Report number: CPH-SYM-DNRF92 MSC Class: 57N70; 58D05; 55R40

  60. On the Balmer spectrum for compact Lie groups

    Authors: Tobias Barthel, J. P. C. Greenlees, Markus Hausmann

    Abstract: We study the Balmer spectrum of the category of finite G-spectra for a compact Lie group G, extending the work for finite G by Strickland, Balmer-Sanders, Barthel-Hausmann-Naumann-Nikolaus-Noel-Stapleton and others. We give a description of the underlying set of the spectrum and show that the Balmer topology is completely determined by the inclusions between the prime ideals and the topology on th… ▽ More

    Submitted 25 July, 2019; v1 submitted 10 October, 2018; originally announced October 2018.

    Comments: Revised version, to appear in Compositio Mathematica

    Report number: CPH-SYM-DNRF92

    Journal ref: Compositio Math. 156 (2020) 39-76

  61. Comparison and Continuity of Wick-type Star Products on certain coadjoint orbits

    Authors: Chiara Esposito, Philipp Schmitt, Stefan Waldmann

    Abstract: In this paper we discuss continuity properties of the Wick-type star product on the 2-sphere, interpreted as a coadjoint orbit. Star products on coadjoint orbits in general have been constructed by different techniques. We compare the constructions of Alekseev-Lachowska and Karabegov and we prove that they agree in general. In the case of the 2-sphere we establish the continuity of the star produc… ▽ More

    Submitted 21 September, 2018; originally announced September 2018.

    Comments: 26 pages. Comments are welcome!

    Report number: CPH-SYM-DNRF92

    Journal ref: Forum Math. (2019) Vol. 31, Issue 5. Pages 1203-1223

  62. arXiv:1808.09832  [pdf, ps, other

    math.AT math.RT

    Idempotent characters and equivariantly multiplicative splittings of K-theory

    Authors: Benjamin Böhme

    Abstract: We classify the primitive idempotents of the $p$-local complex representation ring of a finite group $G$ in terms of the cyclic subgroups of order prime to $p$ and show that they all come from idempotents of the Burnside ring. Our results hold without adjoining roots of unity or inverting the order of $G$, thus extending classical structure theorems. We then derive explicit group-theoretic obstruc… ▽ More

    Submitted 16 April, 2020; v1 submitted 29 August, 2018; originally announced August 2018.

    Comments: 19 pages. Comments welcome! v2: Updated references. Removed a lemma that is no longer relevant. v3: Changes in response to a referee report

    Report number: CPH-SYM-DNRF92 MSC Class: 19L47 (Primary); 19A22; 20C15; 55P43; 55P60; 55P91; 55S91 (Secondary)

    Journal ref: Bull. London Math. Soc., 52, 730-745 (2020)

  63. arXiv:1808.06793  [pdf, ps, other

    math.OA math.GR

    C*-stability of discrete groups

    Authors: Søren Eilers, Tatiana Shulman, Adam P. W. Sørensen

    Abstract: A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with respect to some subclass of $C^*$-algebras, e.g. finite dimensional $C^*$-algebras. We provide criteria and invariants for stability of groups and this allows us to c… ▽ More

    Submitted 20 April, 2021; v1 submitted 21 August, 2018; originally announced August 2018.

    Comments: The results in section 4.2 (finitely generated torsion-free 2-step nilpotent groups) have been strengthened slightly. Clarified in the introduction that we only consider unitary group representations. A few misprints fixed. 39 pages

    Report number: CPH-SYM-DNRF92

    Journal ref: Advances in Mathematics, Vol. 373, 2020

  64. Derived completion for comodules

    Authors: Tobias Barthel, Drew Heard, Gabriel Valenzuela

    Abstract: The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to comodule-theoretic completion, construct various local homology spectral sequences, and derive a tilting-theoretic interpretation of local duality for modules. Our resu… ▽ More

    Submitted 17 January, 2019; v1 submitted 1 August, 2018; originally announced August 2018.

    Comments: Final version to appear in manuscripta mathematica. A preliminary version of the results in the first two sections of this article was previously contained in the joint work of the authors at arXiv:1511.03526

    Report number: CPH-SYM-DNRF92 MSC Class: 55P60 (13D45; 14B15; 55U35)

  65. arXiv:1807.11539  [pdf, ps, other

    math.AT math.GT

    Characteristic numbers of manifold bundles over surfaces with highly connected fibers

    Authors: Manuel Krannich, Jens Reinhold

    Abstract: We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine the characteristic numbers realized by total spaces of bundles of this type, deduce divisibility… ▽ More

    Submitted 16 March, 2020; v1 submitted 30 July, 2018; originally announced July 2018.

    Comments: 23 pages, major revision (included results for topological bundles, removed technical condition in main results, simplified sections 1 and 3), to appear in Journal of the London Mathematical Society

    Report number: CPH-SYM-DNRF92 MSC Class: 57R20; 57R75; 55R10; 55R40

    Journal ref: J. Lond. Math. Soc. (2) 102 (2020), no. 2, 879-904

  66. arXiv:1807.06922  [pdf, ps, other

    math.KT math.DS

    A note on homology for Smale spaces

    Authors: Valerio Proietti

    Abstract: We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple convergence theorem for spectral sequences can be used to prove that all complexes yield the same homology. Furthermore, we introduce a simplicial framework by which the various complexes can be understood as suitable "symm… ▽ More

    Submitted 30 January, 2019; v1 submitted 18 July, 2018; originally announced July 2018.

    Comments: 23 pages, 3 figures, to appear in Groups, Geometry, and Dynamics

    Report number: CPH-SYM-DNRF92 MSC Class: 18G35 (Primary) 37B10; 18G05 (Secondary)

    Journal ref: Groups, Geometry, and Dynamics 14-3 (2020) 813-836

  67. arXiv:1807.06864  [pdf, ps, other

    math.AT math.KT

    Commuting matrices and Atiyah's Real K-theory

    Authors: Simon Gritschacher, Markus Hausmann

    Abstract: We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K-theory.

    Submitted 22 March, 2019; v1 submitted 18 July, 2018; originally announced July 2018.

    Comments: Minor changes. To appear in Journal of Topology

    Report number: CPH-SYM-DNRF92

  68. Index theory on the Miščenko bundle

    Authors: Jens Kaad, Valerio Proietti

    Abstract: We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-product presentation for the module of sections associated to the Miščenko line bundle. In addition, we give a proof of Atiyah's $L^2$-index theorem in the general context of principal bundles over compact Hausdorff spaces.… ▽ More

    Submitted 5 March, 2020; v1 submitted 16 July, 2018; originally announced July 2018.

    Comments: 24 pages, to appear in Kyoto Journal of Mathematics

    Report number: CPH-SYM-DNRF92 MSC Class: 19K35 (Primary) 19K56; 46L85 (Secondary)

    Journal ref: Kyoto J. Math. 62, no. 1 (2022), 103-131

  69. Almost finiteness and the small boundary property

    Authors: David Kerr, Gabor Szabo

    Abstract: Working within the framework of free actions of countable amenable groups on compact metrizable spaces, we show that the small boundary property is equivalent to a density version of almost finiteness, which we call almost finiteness in measure, and that under this hypothesis the properties of almost finiteness, comparison, and $m$-comparison for some nonnegative integer $m$ are all equivalent. Th… ▽ More

    Submitted 11 June, 2019; v1 submitted 11 July, 2018; originally announced July 2018.

    Comments: 32 pages, minor changes

    Report number: CPH-SYM-DNRF92

    Journal ref: Comm. Math. Phys. 374 (2020), pp. 1--31

  70. Actions of certain torsion-free elementary amenable groups on strongly self-absorbing C*-algebras

    Authors: Gabor Szabo

    Abstract: In this paper we consider a bootstrap class $\mathfrak C$ of countable discrete groups, which is closed under countable unions and extensions by the integers, and we study actions of such groups on C*-algebras. This class includes all torsion-free abelian groups, poly-$\mathbb Z$-groups, as well as other examples. Using the interplay between relative Rokhlin dimension and semi-strongly self-absorb… ▽ More

    Submitted 9 July, 2018; originally announced July 2018.

    Comments: 17 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55; 46L40

    Journal ref: Comm. Math. Phys. 371 (2019), no. 1, pp. 267--284

  71. Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla

    Authors: Magdalena Musat, Mikael Rørdam

    Abstract: We show that there exist factorizable quantum channels in each dimension $\ge 11$ which do not admit a factorization through any finite dimensional von Neumann algebra, and do require ancillas of type II$_1$, thus witnessing new infinite-dimensional phenomena in quantum information theory. We show that the set of n by n matrices of correlations arising as second-order moments of projections in fin… ▽ More

    Submitted 13 March, 2019; v1 submitted 26 June, 2018; originally announced June 2018.

    Comments: 16 pages. An appendix by Narutaka Ozawa has been added. To appear in Comm. Math. Phys

    Report number: CPH-SYM-DNRF92 MSC Class: 46L10; 81P45; 47L90

  72. arXiv:1805.12466  [pdf, ps, other

    math.AT math.CT

    Strictifying Homotopy Coherent Actions on Hochschild Complexes

    Authors: Espen Auseth Nielsen

    Abstract: If P is a dg-operad acting on a dg-algebra A via algebra homomorphisms, then P acts on the Hochschild complex of A. In the more general case when P is a dg-prop, we show that P still acts on the Hochschild complex, but only up to coherent homotopy. We moreover give a functorial dg-replacement of P that strictifies the action. As an application, we obtain an explicit strictification of the homotopy… ▽ More

    Submitted 14 December, 2018; v1 submitted 31 May, 2018; originally announced May 2018.

    Comments: Version 2: Corrected typographical errors and added additional details

    Report number: CPH-SYM-DNRF92 MSC Class: 13D03; 16E35; 18D05; 18D10

  73. arXiv:1805.10751  [pdf, ps, other

    math.RT math.AG math.CT

    Completing perfect complexes

    Authors: Tobias Barthel, Bernhard Keller, Henning Krause

    Abstract: This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented modules over a right coherent ring is the completion of the category of perfect complexes. The result extends to non-affine noetherian schemes and gives rise to a… ▽ More

    Submitted 30 October, 2019; v1 submitted 27 May, 2018; originally announced May 2018.

    Comments: 35 pages, with appendices by Tobias Barthel, Henning Krause and Bernhard Keller. Version 3: Added a new appendix by Tobias Barthel and Henning Krause that refines for a separated noetherian scheme the results of the main text. Added a discussion of completions of abelian categories and their derived categories. Version 4: Minor revision, correcting some examples

    Report number: CPH-SYM-DNRF92 MSC Class: 18E30 (primary); 14F05; 16E35; 55P42 (secondary)

  74. arXiv:1805.09541  [pdf, ps, other

    math.AG

    Weak Algebra Bundles and Associator Varieties

    Authors: Clarisson Rizzie Canlubo

    Abstract: Algebra bundles, in the strict sense, appear in many areas of geometry and physics. However, the structure of an algebra is flexible enough to vary non-trivially over a connected base, giving rise to a structure of a weak algebra bundle. We will show that the notion of a weak algebra bundle is more natural than that of a strict algebra bundle. We will give necessary and sufficient conditions for w… ▽ More

    Submitted 22 November, 2018; v1 submitted 24 May, 2018; originally announced May 2018.

    Report number: CPH-SYM-DNRF92 MSC Class: 14D20; 55R50; 17B63; 53D17

  75. $C^*$-simplicity and representations of topological full groups of groupoids

    Authors: Kevin Aguyar Brix, Eduardo Scarparo

    Abstract: Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show that the image of this representation generates $C^*(G)$ if and only if $C^*(G)$ admits no tracial state. The techniques that we use include the notion of groups covering groupoids. As an application, we… ▽ More

    Submitted 23 June, 2019; v1 submitted 17 May, 2018; originally announced May 2018.

    Comments: 13 pages. Minor changes, including new references. Accepted in Journal of Functional Analysis

    Report number: CPH-SYM-DNRF92

    Journal ref: Journal of Functional Analysis Volume 277, Issue 9, 1 November 2019, Pages 2981-2996

  76. arXiv:1803.11075  [pdf, ps, other

    math.OA

    Fixed-points in the cone of traces on a C*-algebra

    Authors: Mikael Rordam

    Abstract: Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a non-zero fixed point whenever acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod's results sa… ▽ More

    Submitted 2 January, 2019; v1 submitted 29 March, 2018; originally announced March 2018.

    Comments: 31 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L35; 46L05; 37A55

  77. arXiv:1803.10897  [pdf, ps, other

    math.KT math.AT

    K-theory and topological cyclic homology of henselian pairs

    Authors: Dustin Clausen, Akhil Mathew, Matthew Morrow

    Abstract: Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity theorem (for mod $n$ coefficients, with $n$ invertible in $R$) and McCarthy's theorem on relative… ▽ More

    Submitted 20 July, 2020; v1 submitted 28 March, 2018; originally announced March 2018.

    Comments: 59 pages, revised and final version

    Report number: CPH-SYM-DNRF92

  78. arXiv:1803.06679  [pdf, ps, other

    math.GR math.OA

    Kirchberg--Wassermann exactness vs exactness: reduction to the unimodular totally disconnected case

    Authors: Chris Cave, Joachim Zacharias

    Abstract: We show that in order to prove that every second countable locally compact groups with exact reduced group C*-algebra is exact in the dynamical sense (i.e. KW-exact) it suffices to show this for totally disconnected groups.

    Submitted 18 March, 2018; originally announced March 2018.

    Comments: 7 pages

    Report number: CPH-SYM-DNRF92

  79. arXiv:1803.06325  [pdf, ps, other

    math.AT

    Lie algebras and $v_n$-periodic spaces

    Authors: Gijs Heuts

    Abstract: We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this $v_n$-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare… ▽ More

    Submitted 29 October, 2020; v1 submitted 16 March, 2018; originally announced March 2018.

    Comments: Final version to appear in Annals of Mathematics. Added a short section on the Whitehead bracket

    Report number: CPH-SYM-DNRF92

  80. arXiv:1803.03083  [pdf, other

    math.CO

    Equivariant Euler characteristics of the symplectic building

    Authors: Jesper Michael Møller

    Abstract: We determine the equivariant Euler characteristics for the action of a finite symplectic group on its building.

    Submitted 18 March, 2020; v1 submitted 8 March, 2018; originally announced March 2018.

    Comments: First revision

    Report number: CPH-SYM-DNRF92

  81. On characteristic classes of exotic manifold bundles

    Authors: Manuel Krannich

    Abstract: Given a closed simply connected manifold $M$ of dimension $2n\ge6$, we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the analogous ring resulting from replacing $M$ by the connected sum $M\sharpΣ$ with an exotic sphere $Σ$. We show that, after inverting the order of $Σ$ in the group of homotopy spheres, the two rings in question are isomorphic in a range o… ▽ More

    Submitted 15 May, 2019; v1 submitted 7 February, 2018; originally announced February 2018.

    Comments: 16 pages, to appear in Mathematische Annalen

    Report number: CPH-SYM-DNRF92 MSC Class: 55R40; 57R60; 57S05; 55N22

    Journal ref: Math. Ann. 379, 1-21 (2021)

  82. Multiplicativity of the idempotent splittings of the Burnside ring and the G-sphere spectrum

    Authors: Benjamin Böhme

    Abstract: We provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the G-equivariant sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any finite group. Our results describe explicitly how these structures depend on the subgroup lattice and conjugation in G. Algebraically, our analysis characterizes the mult… ▽ More

    Submitted 4 March, 2019; v1 submitted 6 February, 2018; originally announced February 2018.

    Comments: 36 pages. v2: Slightly simpler (but equivalent) reformulation of main theorem. Revisions in response to my PhD committee's report and a referee report. v3: Final version, to appear in "Advances in Mathematics"

    Report number: CPH-SYM-DNRF92 MSC Class: 55P91 (Primary); 55P43; 55Q91; 55S91; 19A22 (Secondary)

    Journal ref: Adv. Math. 347 (2019), 904-939

  83. arXiv:1712.07633  [pdf, ps, other

    math.AT

    On the comparison of stable and unstable $p$-completion

    Authors: Tobias Barthel, A. K. Bousfield

    Abstract: In this note we show that a $p$-complete nilpotent space $X$ has a $p$-complete suspension spectrum if and only if its homotopy groups $π_*X$ are bounded $p$-torsion. In contrast, if $π_*X$ is not all bounded $p$-torsion, we locate uncountable rational vector spaces in the integral homology and in the stable homotopy groups of $X$. To prove this, we establish a homological criterion for $p$-comple… ▽ More

    Submitted 20 December, 2017; originally announced December 2017.

    Comments: All comments welcome

    Report number: CPH-SYM-DNRF92

  84. Conservative descent for semi-orthogonal decompositions

    Authors: Daniel Bergh, Olaf M. Schnürer

    Abstract: Motivated by the local flavor of several well-known semi-orthogonal decompositions in algebraic geometry, we introduce a technique called conservative descent, which shows that it is enough to establish these decompositions locally. The decompositions we have in mind are those for projectivized vector bundles and blow-ups, due to Orlov, and root stacks, due to Ishii and Ueda. Our technique simplif… ▽ More

    Submitted 19 December, 2019; v1 submitted 19 December, 2017; originally announced December 2017.

    Comments: Final version

    Report number: CPH-SYM-DNRF92

    Journal ref: Advances in Mathematics, Volume 360, 22 January 2020, 106882, ISSN 0001-8708

  85. arXiv:1712.06469  [pdf, ps, other

    math.AT math.CT

    $\infty$-Operads as Analytic Monads

    Authors: David Gepner, Rune Haugseng, Joachim Kock

    Abstract: We develop an $\infty$-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\infty$-operads, namely $\infty$-operads as analytic monads. We justify this definition by proving that the $\infty$-category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equi… ▽ More

    Submitted 29 October, 2020; v1 submitted 18 December, 2017; originally announced December 2017.

    Comments: 69 pages, v2: updated using results of arXiv:2002.01037, v3: accepted version

    Report number: CPH-SYM-DNRF92

  86. arXiv:1712.05285  [pdf, ps, other

    math.OA math-ph math.QA

    On the complete boundedness of the Schur block product

    Authors: Erik Christensen

    Abstract: We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_{ij}), B:= (b_{ij}): A (*) B := (a_{ij}b_{ij}) = V* pi(A) F pi(B) V, such that V is an isometry, pi is a *-representation and F is a self-adjoint unitary. This implies an inequality due to Livshits and two ap… ▽ More

    Submitted 8 November, 2018; v1 submitted 14 December, 2017; originally announced December 2017.

    Comments: 10 p, revised, expanded and to appear in Proc. AMS

    Report number: CPH-SYM-DNRF92 MSC Class: 15A69; 46L07; 81P68

  87. arXiv:1712.03189  [pdf, ps, other

    math.AT math.KT

    Verschiebung maps among $K$-groups of truncated polynomial algebras

    Authors: Ryo Horiuchi

    Abstract: Let $p$ be a prime number, and let $A$ be a ring in which $p$ is nilpotent. In this paper, we consider the maps $$K_{q+1}(A[x]/(x^m), (x))\to K_{q+1}(A[x]/(x^{mn}), (x)),$$induced by the ring homomorphism $A[x]/(x^{m})\to A[x]/(x^{mn})$, $x\mapsto x^n$. We evaluate these maps, up to extension, for general $A$ in terms of topological Hochschild homology, and for regular $\mathbb{F}_p$-algebras $A$,… ▽ More

    Submitted 20 January, 2018; v1 submitted 8 December, 2017; originally announced December 2017.

    Comments: Corollary 4.7 in the previous version is deleted. Two new corollaries are added

    Report number: CPH-SYM-DNRF92

  88. arXiv:1712.03187  [pdf, ps, other

    math.AT math.KT math.NT

    The non-nil-invariance of TP

    Authors: Ryo Horiuchi

    Abstract: Hesselholt defined a spectrum $\operatorname{TP}(X)$, the periodic topological cyclic homology of a scheme $X$, using topological Hochschild homology and the Tate construction, which is a topological analogue of Connes-Tsygan periodic cyclic homology $\operatorname{HP}$ defined by Hochschild homology and the Tate construction. Goodwillie proved that for $R$ an algebra over a field of characteristi… ▽ More

    Submitted 7 November, 2018; v1 submitted 8 December, 2017; originally announced December 2017.

    Comments: Fixed an error about the degrees of truncation in Theorem 1.1 and added Corollary 3.4

    Report number: CPH-SYM-DNRF92

  89. Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids

    Authors: Kevin Aguyar Brix, Toke Meier Carlsen

    Abstract: A one-sided shift of finite type $(X_A,σ_A)$ determines on the one hand a Cuntz-Krieger algebra $\mathcal{O}_A$ with a distinguished abelian subalgebra $\mathcal{D}_A$ and a certain completely positive map $τ_A$ on $\mathcal{O}_A$. On the other hand, $(X_A,σ_A)$ determines a groupoid $\mathcal{G}_A$ together with a certain homomorphism $ε_A$ on $\mathcal{G}_A$. We show that this data completely ch… ▽ More

    Submitted 19 February, 2019; v1 submitted 30 November, 2017; originally announced December 2017.

    Comments: v2: Minor changes, corollary added, references updated; 9 pages. This is the version that will be published

    Report number: CPH-SYM-DNRF92

    Journal ref: J. Aust. Math. Soc. 109 (2020), no. 3, 289-298

  90. arXiv:1711.10442  [pdf, other

    math.OA math.GR

    C*-simplicity of HNN extensions and groups acting on trees

    Authors: Rasmus Sylvester Bryder, Nikolay A. Ivanov, Tron Omland

    Abstract: We study non-ascending HNN extensions acting on their Bass-Serre trees, and characterize C*-simplicity and the unique trace property by means of the kernel and quasi-kernels of the HNN extension in question. We also present a concrete example of an HNN extension that is a new example of a group that is not C*-simple but does have the unique trace property. Additionally, we include certain more gen… ▽ More

    Submitted 12 April, 2019; v1 submitted 28 November, 2017; originally announced November 2017.

    Comments: 30 pages; several modifications to the presentation have been made, while the content remains essentially unchanged; to appear in Ann. Inst. Fourier

    Report number: CPH-SYM-DNRF92 MSC Class: 22D25; 20E06 (Primary) 46L05; 20E08 (Secondary)

  91. arXiv:1711.10226  [pdf, ps, other

    math.AT math.KT

    Real topological Hochschild homology

    Authors: Emanuele Dotto, Kristian Moi, Irakli Patchkoria, Sune Precht Reeh

    Abstract: This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably multiplicative. We then calculate its geometric fixed points and its Mackey functor of components, and show a decomposition result for group-algebras. Using these structu… ▽ More

    Submitted 28 November, 2017; originally announced November 2017.

    Report number: CPH-SYM-DNRF92 MSC Class: 19D55; 55P91; 55P43; 11E70

    Journal ref: J. Eur. Math. Soc. (JEMS) 23 (2021), no. 1, 63-152

  92. arXiv:1711.03491  [pdf, ps, other

    math.AT math.GR math.RT

    Stratification and duality for homotopical groups

    Authors: Tobias Barthel, Natalia Castellana, Drew Heard, Gabriel Valenzuela

    Abstract: We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of module spectra over $C^*(B\mathcal{G},\mathbb{F}_p)$ is stratified and costratified for a large class of $p$-local compact groups $\mathcal{G}$ including compact… ▽ More

    Submitted 5 July, 2019; v1 submitted 9 November, 2017; originally announced November 2017.

    Comments: Corrected discussion of Chouinard's theorem for homotopical groups; accepted for publication in Advances in Mathematics

    Report number: CPH-SYM-DNRF92

  93. arXiv:1711.00844  [pdf, other

    math.AT math.CT

    Chromatic homotopy theory is asymptotically algebraic

    Authors: Tobias Barthel, Tomer Schlank, Nathaniel Stapleton

    Abstract: Inspired by the Ax--Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the approximation problem in chromatic homotopy theory. More precisely, we show that the ultraproduct of the $E(n,p)$-local categories over any non-prinicipal ultra… ▽ More

    Submitted 19 January, 2020; v1 submitted 2 November, 2017; originally announced November 2017.

    Comments: Minor changes, to appear in Inventiones Mathematicae

    Report number: CPH-SYM-DNRF92

  94. Homological stability of topological moduli spaces

    Authors: Manuel Krannich

    Abstract: Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for the graded pieces of the module with respect to constant and abelian coefficients. We furthermore introduce a notion of coefficient systems of finite degree in… ▽ More

    Submitted 2 January, 2019; v1 submitted 23 October, 2017; originally announced October 2017.

    Comments: 42 pages, 8 figures, to appear in Geometry & Topology

    Report number: CPH-SYM-DNRF92 MSC Class: 55P48; 55R40; 55R80; 57R19

    Journal ref: Geom. Topol. 23 (2019) 2397-2474

  95. arXiv:1709.06839  [pdf, other

    math.AT math.DG math.GT

    Product and coproduct in string topology

    Authors: Nancy Hingston, Nathalie Wahl

    Abstract: Let M be a closed Riemannian manifold. We extend the product of Goresky-Hingston, on the cohomology of the free loop space of M relative to the constant loops, to a nonrelative product. It is graded associative and commutative, and compatible with the length filtration on the loop space, like the original product. We prove the following new geometric property of the dual homology coproduct: the no… ▽ More

    Submitted 28 January, 2022; v1 submitted 20 September, 2017; originally announced September 2017.

    Comments: Final version, to appear in Ann. Scient. Ec. Norm. Sup

    Report number: CPH-SYM-DNRF92, CPH-GEOTOP-DNRF151

  96. The Balmer spectrum of the equivariant homotopy category of a finite abelian group

    Authors: Tobias Barthel, Markus Hausmann, Niko Naumann, Thomas Nikolaus, Justin Noel, Nathaniel Stapleton

    Abstract: For a finite abelian group $A$, we determine the Balmer spectrum of $\mathrm{Sp}_A^ω$, the compact objects in genuine $A$-spectra. This generalizes the case $A=\mathbb{Z}/p\mathbb{Z}$ due to Balmer and Sanders \cite{Balmer-Sanders}, by establishing (a corrected version of) their log$_p$-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and esta… ▽ More

    Submitted 7 December, 2018; v1 submitted 14 September, 2017; originally announced September 2017.

    Comments: v3: minor changes, to appear in Inventiones Mathematicae

    Report number: CPH-SYM-DNRF92 MSC Class: 55

    Journal ref: Invent. Math. 216 (2019), 215-240

  97. arXiv:1709.00620  [pdf, ps, other

    math.AG

    Categorical measures for finite group actions

    Authors: Daniel Bergh, Sergey Gorchinskiy, Michael Larsen, Valery Lunts

    Abstract: Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases, these two measures coincide. This implies, in particular, a conjecture of Galkin and Shinder on categori… ▽ More

    Submitted 2 September, 2017; originally announced September 2017.

    Comments: 55 pages. Comments are welcome

    Report number: CPH-SYM-DNRF92

  98. arXiv:1708.09632  [pdf, other

    math.AT math.CT

    $\infty$-operads via symmetric sequences

    Authors: Rune Haugseng

    Abstract: We construct a generalization of the Day convolution tensor product of presheaves that works for certain double $\infty$-categories. Using this construction, we obtain an $\infty$-categorical version of the well-known description of (one-object) operads as associative algebras in symmetric sequences; more generally, we show that (enriched) $\infty$-operads with varying spaces of objects can be des… ▽ More

    Submitted 12 March, 2021; v1 submitted 31 August, 2017; originally announced August 2017.

    Comments: 50 pages. v2: Substantially rewritten with an improved version of the Day convolution construction, which produces a double $\infty$-category, v3: Various corrections

    Report number: CPH-SYM-DNRF92

  99. arXiv:1708.09261  [pdf, ps, other

    math.AT math.AG

    Algebraic chromatic homotopy theory for $BP_*BP$-comodules

    Authors: Tobias Barthel, Drew Heard

    Abstract: In this paper, we study the global structure of an algebraic avatar of the derived category of ind-coherent sheaves on the moduli stack of formal groups. In analogy with the stable homotopy category, we prove a version of the nilpotence theorem as well as the chromatic convergence theorem, and construct a generalized chromatic spectral sequence. Furthermore, we discuss analogs of the telescope con… ▽ More

    Submitted 30 August, 2017; originally announced August 2017.

    Comments: All comments welcome

    Report number: CPH-SYM-DNRF92

  100. On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras

    Authors: Selçuk Barlak, Gábor Szabó

    Abstract: We show that an outer action of a finite abelian group on a simple Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if the action is given by diagonal quasi-free automorphisms and the associated matrix is aperiodic. This is achieved by an approximate cohomology vanishing-type argument for the canonical shift restricted to the relative commutant of the set of domain proje… ▽ More

    Submitted 3 October, 2018; v1 submitted 28 August, 2017; originally announced August 2017.

    Comments: v3 17 pages; this version has been accepted for publication in Mathematica Scandinavica

    Report number: CPH-SYM-DNRF92 MSC Class: 46L40; 46L55

    Journal ref: Math. Scand. 125 (2019), no. 2, pp. 210--226

  101. The embedding problem in topological dynamics and Takens' theorem

    Authors: Yonatan Gutman, Yixiao Qiao, Gabor Szabo

    Abstract: We prove that every $\mathbb{Z}^{k}$-action $(X,\mathbb{Z}^{k},T)$ of mean dimension less than $D/2$ admitting a factor $(Y,\mathbb{Z}^{k},S)$ of Rokhlin dimension not greater than $L$ embeds in $(([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}\times Y,σ\times S)$, where $D\in\mathbb{N}$, $L\in\mathbb{N}\cup\{0\}$ and $σ$ is the shift on the Hilbert cube $([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}$; in particular, when… ▽ More

    Submitted 8 December, 2017; v1 submitted 20 August, 2017; originally announced August 2017.

    Comments: 26 pages; this version is going to appear in Nonlinearity

    Report number: CPH-SYM-DNRF92 MSC Class: 37C45; 54H20

    Journal ref: Nonlinearity 31 (2018), no. 2, pp. 597--620

  102. arXiv:1707.08049  [pdf, ps, other

    math.AT math.CT

    Enriched $\infty$-operads

    Authors: Hongyi Chu, Rune Haugseng

    Abstract: In this paper we initiate the study of enriched $\infty$-operads. We introduce several models for these objects, including enriched versions of Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and Moerdijk, and show these are equivalent. Our main results are a version of Rezk's completion theorem for enriched $\infty$-operads: localization at the fully faithful and essentially s… ▽ More

    Submitted 14 November, 2019; v1 submitted 25 July, 2017; originally announced July 2017.

    Comments: Accepted version, 59 pages

    Report number: CPH-SYM-DNRF92

  103. arXiv:1707.07862  [pdf, other

    math.AT math.KT

    Comparing cyclotomic structures on different models for topological Hochschild homology

    Authors: Emanuele Dotto, Cary Malkiewich, Irakli Patchkoria, Steffen Sagave, Calvin Woo

    Abstract: The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying Bökstedt's original definition of $THH$ to $A$. In this paper, we construct a chain of stable equivalences of cyclotomic spectra comparing these two models for $THH(A)$. This implies that the two versions of topological cyclic homology resul… ▽ More

    Submitted 31 May, 2019; v1 submitted 25 July, 2017; originally announced July 2017.

    Comments: v2: 26 pages, exposition improved. Accepted for publication by the Journal of Topology

    Report number: CPH-SYM-DNRF92 MSC Class: 19D55; 55Q91; 55P43

    Journal ref: Journal of Topology, 12 (2019), no. 4, 1146-1173

  104. Rational Homological Stability for Automorphisms of Manifolds

    Authors: Matthias Grey

    Abstract: We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, but need to satisfy a certain connectivity assumption. The main theorems of this paper extend homological stability results for automorphism spaces of connected sums of products of spheres of the same dimension b… ▽ More

    Submitted 23 July, 2017; originally announced July 2017.

    Report number: CPH-SYM-DNRF92

    Journal ref: Algebr. Geom. Topol. 19 (2019) 3359-3407

  105. Weak factorization and the Grothendieck group of Deligne-Mumford stacks

    Authors: Daniel Bergh

    Abstract: We construct a presentation for the Grothendieck group of Deligne-Mumford stacks over a field of characteristic zero. The generators for this presentation are smooth, proper Deligne-Mumford stacks and the relations are expressed in terms of stacky blow-ups. In the process we prove a version of the weak factorization theorem for Deligne-Mumford stacks.

    Submitted 11 October, 2018; v1 submitted 19 July, 2017; originally announced July 2017.

    Comments: Final version

    Report number: CPH-SYM-DNRF92 MSC Class: 14A20; 14E05; 14F42

    Journal ref: Advances in Mathematics, Volume 340, 2018, Pages 193-210

  106. arXiv:1707.05986  [pdf, ps, other

    math.AT

    Monadicity of the Bousfield-Kuhn functor

    Authors: Rosona Eldred, Gijs Heuts, Akhil Mathew, Lennart Meier

    Abstract: We consider the localization of the $\infty$-category of spaces at the $v_n$-periodic equivalences, the case $n=0$ being rational homotopy theory. We prove that this localization is for $n\geq 1$ equivalent to algebras over a certain monad on the $\infty$-category of $T(n)$-local spectra. This monad is built from the Bousfield--Kuhn functor.

    Submitted 19 July, 2017; originally announced July 2017.

    Comments: 8 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 55Q51; 55P60

  107. arXiv:1707.00850  [pdf, other

    math.CO

    Equivariant Euler characteristics of the unitary building

    Authors: Jesper M. Møller

    Abstract: We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.

    Submitted 17 March, 2020; v1 submitted 4 July, 2017; originally announced July 2017.

    Comments: First revision

    Report number: CPH-SYM-DNRF92 MSC Class: 05A15

  108. arXiv:1706.00208  [pdf, ps, other

    math.AT math.AC

    Excellent rings in transchromatic homotopy theory

    Authors: Tobias Barthel, Nathaniel Stapleton

    Abstract: The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard techniques from commutative algebra. In particular, we show that the coefficients of iterated localizations of Morava $E$-theory at the Morava $K$-theories are normal domains and also that the coefficients in the transchrom… ▽ More

    Submitted 1 June, 2017; originally announced June 2017.

    Comments: All comments welcome

    Report number: CPH-SYM-DNRF92

  109. arXiv:1705.08875  [pdf, ps, other

    math.AG

    Tautological classes with twisted coefficients

    Authors: Dan Petersen, Mehdi Tavakol, Qizheng Yin

    Abstract: Let $M_g$ be the moduli space of smooth genus $g$ curves. We define a notion of Chow groups of $M_g$ with coefficients in a representation of $Sp(2g)$, and we define a subgroup of tautological classes in these Chow groups with twisted coefficients. Studying the tautological groups of $M_g$ with twisted coefficients is equivalent to studying the tautological rings of all fibered powers $C_g^n$ of t… ▽ More

    Submitted 9 April, 2020; v1 submitted 24 May, 2017; originally announced May 2017.

    Comments: 50 pages. v2, exposition clarified, Section 12 rewritten. Final version to appear in Annales de l'ENS

    Report number: CPH-SYM-DNRF92 MSC Class: 14H10; 14C25; 14C17; 18D10; 55R35

    Journal ref: Ann. Sci. Éc. Norm. Supér. (4) 54 (2021), no. 5, 1179-1236

  110. On the $C^*$-algebra generated by the Koopman representation of a topological full group

    Authors: Eduardo Scarparo

    Abstract: Let $(X,T,μ)$ be a Cantor minimal sytem and $[[T]]$ the associated topological full group. We analyze $C^*_π([[T]])$, where $π$ is the Koopman representation attached to the action of $[[T]]$ on $(X,μ)$. Specifically, we show that $C^*_π([[T]])=C^*_π([[T]]')$ and that the kernel of the character $τ$ on $C^*_π([[T]])$ coming from weak containment of the trivial representation is a hereditary… ▽ More

    Submitted 3 March, 2019; v1 submitted 22 May, 2017; originally announced May 2017.

    Comments: 9 pages

    Report number: CPH-SYM-DNRF92

    Journal ref: Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 3 (2019), 469-479

  111. Gross-Hopkins Duals of Higher Real K-theory Spectra

    Authors: Tobias Barthel, Agnes Beaudry, Vesna Stojanoska

    Abstract: We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain finite subgroups $G$ of the Morava stabilizer group, the homotopy fixed point spectra $E_n^{hG}$ are Gross-Hopkins self-dual up to a shift. In this paper, we de… ▽ More

    Submitted 16 June, 2020; v1 submitted 19 May, 2017; originally announced May 2017.

    Report number: CPH-SYM-DNRF92 MSC Class: 55P99

    Journal ref: Trans. Amer. Math. Soc., Volume 372, Number 5, 1 September 2019, Pages 3347-3368

  112. arXiv:1705.04500  [pdf, ps, other

    math.OA math.DS

    On nuclearity and exactness of the tame C*-algebras associated with finitely separated graphs

    Authors: Matias Lolk

    Abstract: We introduce a graph theoretic property called Condition (N) for finitely separated graphs and prove that it is equivalent to both nuclearity and exactness of the associated universal tame graph C*-algebra.

    Submitted 12 May, 2017; originally announced May 2017.

    Comments: 30 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55

  113. arXiv:1705.04495  [pdf, ps, other

    math.OA math.RA

    Convex subshifts, separated Bratteli diagrams, and ideal structure of tame separated graph algebras

    Authors: Pere Ara, Matias Lolk

    Abstract: We introduce a new class of partial actions of free groups on totally disconnected compact Hausdorff spaces, which we call convex subshifts. These serve as an abstract framework for the partial actions associated with finite separated graphs in much the same way as classical subshifts generalize the edge shift of a finite graph. We define the notion of a finite type convex subshift and show that a… ▽ More

    Submitted 12 May, 2017; originally announced May 2017.

    Comments: 60 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 16D25; 46L55

  114. arXiv:1705.04494  [pdf, ps, other

    math.OA math.RA

    Exchange rings and real rank zero C*-algebras associated with finitely separated graphs

    Authors: Matias Lolk

    Abstract: We introduce a generalisation of Condition (K) to finitely separated graphs and show that it is equivalent to essential freeness of the associated partial action as well as the exchange property of any of the associated tame algebras. As a consequence, we can show that any tame separated graph algebra with the exchange property is separative.

    Submitted 12 May, 2017; originally announced May 2017.

    Comments: 41 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55; 16D25; 16D70

  115. arXiv:1705.03855  [pdf, ps, other

    math.AT math.KT

    Rigidity and exotic models for $v_1$-local $G$-equivariant stable homotopy theory

    Authors: Irakli Patchkoria, Constanze Roitzheim

    Abstract: We prove that the $v_1$-local $G$-equivariant stable homotopy category for $G$ a finite group has a unique $G$-equivariant model at $p=2$. This means that at the prime $2$ the homotopy theory of $G$-spectra up to fixed point equivalences on $K$-theory is uniquely determined by its triangulated homotopy category and basic Mackey structure. The result combines the rigidity result for $K$-local spect… ▽ More

    Submitted 10 May, 2017; originally announced May 2017.

    Comments: 34 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 55P91; 55P42; 18G55

  116. arXiv:1705.02818  [pdf, ps, other

    math.OA

    Just-infinite C*-algebras and their invariants

    Authors: Mikael Rordam

    Abstract: Just-infinite C*-algebras, i.e., infinite dimensional C*-algebras, whose proper quotients are finite dimensional, were investigated in [Grigorchuk-Musat-Rordam, 2016]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in that article. In this paper we extend that construction by showing that each infinite dimensional metrizable Choquet simplex is a… ▽ More

    Submitted 28 December, 2017; v1 submitted 8 May, 2017; originally announced May 2017.

    Comments: 22 pages. A more detailed proof of Proposition 2.2 is included in this version, and a missing condition in Proposition 2.2 (and Corollary 2.3) is added. To appear in Int. Math. Res. Not. IMRN

    Report number: CPH-SYM-DNRF92 MSC Class: 46L05; 46L35; 46L45

  117. Hyperbolic isometries and boundaries of systolic complexes

    Authors: Tomasz Prytuła

    Abstract: Given a group $G$ acting geometrically on a systolic complex $X$ and a hyperbolic isometry $h \in G$, we study the associated action of $h$ on the systolic boundary $\partial X$. We show that $h$ has a canonical pair of fixed points on the boundary and that it acts trivially on the boundary if and only if it is virtually central. The key tool that we use to study the action of $h$ on $\partial X$… ▽ More

    Submitted 2 May, 2017; originally announced May 2017.

    Comments: 34 pages, 4 figures

    Report number: CPH-SYM-DNRF92 MSC Class: 20F67 (Primary) 20F65; 20F69 (Secondary)

  118. arXiv:1705.00198  [pdf, other

    math.GR math.OA

    Computational explorations of the Thompson group T for the amenability problem of F

    Authors: S. Haagerup, U. Haagerup, M. Ramirez-Solano

    Abstract: It is a long standing open problem whether the Thompson group $F$ is an amenable group. In this paper we show that if $A$, $B$, $C$ denote the standard generators of Thompson group $T$ and $D:=C B A^{-1}$ then $$\sqrt2+\sqrt3\,<\,\frac1{\sqrt{12}}||(I+C+C^2)(I+D+D^2+D^3)||\,\le\, 2+\sqrt2.$$ Moreover, the upper bound is attained if the Thompson group $F$ is amenable. Here, the norm of an element i… ▽ More

    Submitted 23 September, 2018; v1 submitted 29 April, 2017; originally announced May 2017.

    Comments: Accepted for publication in the journal Experimental Mathematics. Updated with the referee suggestions

    Report number: CPH-SYM-DNRF92 MSC Class: 20F65; 20-04; 43A07; 22D25; 46L05

  119. arXiv:1704.08548  [pdf, ps, other

    math.KT

    The orbit method for the Baum-Connes Conjecture for algebraic groups over local function fields

    Authors: Siegfried Echterhoff, Kang Li, Ryszard Nest

    Abstract: The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof of the Connes-Kasparov conjecture for almost connected groups \cite{MR2010742} in order to deal with linear algebraic groups over local function fields (i.e., non-archimedean local fields of positive characteristic). As a consequence, we verify the… ▽ More

    Submitted 27 April, 2017; originally announced April 2017.

    Report number: CPH-SYM-DNRF92

    Journal ref: J. Lie Theory 28 (2018), no. 2, 323-341

  120. arXiv:1704.03389  [pdf, other

    math.RT math.AT math.CT math.GR math.QA

    Adams operations and symmetries of representation categories

    Authors: Ehud Meir, Markus Szymik

    Abstract: Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point of view, they codify some of the symmetric monoidal structure of the representation category. We show that the monoidal structure on the category alone, regard… ▽ More

    Submitted 3 June, 2019; v1 submitted 11 April, 2017; originally announced April 2017.

    Comments: 20 pages, Indiana Univ. Math. J. (to appear)

    Report number: CPH-SYM-DNRF92

    Journal ref: Indiana Univ. Math. J. 70 (2021) 501-523

  121. arXiv:1704.02723  [pdf, ps, other

    math.OA

    Injective envelopes and the intersection property

    Authors: Rasmus Sylvester Bryder

    Abstract: We consider the ideal structure of a reduced crossed product of a unital $C^*$-algebra equipped with an action of a discrete group. More specifically we find sufficient and necessary conditions for the group action to have the intersection property, meaning that non-zero ideals in the reduced crossed product restrict to non-zero ideals in the underlying $C^*$-algebra. We show that the intersection… ▽ More

    Submitted 11 November, 2021; v1 submitted 10 April, 2017; originally announced April 2017.

    Comments: To appear in J. Operator Theory. 23 pages; v4; reorganised preliminaries and examples, restructured results

    Report number: CPH-SYM-DNRF92 MSC Class: 22D25; 37A55; 46L55; 46M10; 47L65

  122. arXiv:1703.07842  [pdf, ps, other

    math.KT math.NT

    A K-theoretic approach to Artin maps

    Authors: Dustin Clausen

    Abstract: We define a functorial "Artin map" attached to any small $\bf{Z}$-linear stable $\infty$-category, which in the case of perfect complexes over a global field recovers the usual Artin map from the idele class group to the abelianized absolute Galois group. In particular, this gives a new proof of the Artin reciprocity law.

    Submitted 3 April, 2017; v1 submitted 22 March, 2017; originally announced March 2017.

    Report number: CPH-SYM-DNRF92

  123. arXiv:1701.06788  [pdf, ps, other

    math.AT math.GT

    Three applications of delooping to H-principles

    Authors: Alexander Kupers

    Abstract: In this paper we give three applications of a method to prove h-principles on closed manifolds. Under weaker conditions this method proves a homological h-principle, under stronger conditions it proves a homotopical one. The three applications are as follows: a homotopical version of Vassiliev's h-principle, the contractibility of the space of framed functions, and a version of Mather-Thurston the… ▽ More

    Submitted 6 October, 2018; v1 submitted 24 January, 2017; originally announced January 2017.

    Comments: 51 pages, 8 figures. Many small improvements, no substantial changes to results

    Report number: CPH-SYM-DNRF92 MSC Class: 58D10; 57R45

  124. Equivariant Algebraic Index Theorem

    Authors: Alexander Gorokhovsky, Niek de Kleijn, Ryszard Nest

    Abstract: We prove a Γ-equivariant version of the algebraic index theorem, where Γ is a discrete group of automorphisms of a formal deformation of a symplectic manifold. The particular cases of this result are the algebraic version of the transversal index theorem related to the theorem of A. Connes and H. Moscovici for hypoelliptic operators and the index theorem for the extension of the algebra of pseudod… ▽ More

    Submitted 15 January, 2017; originally announced January 2017.

    Report number: CPH-SYM-DNRF92

    Journal ref: J. Inst. Math. Jussieu 20 (2021) 929-955

  125. arXiv:1701.03411  [pdf, other

    math.CO

    Equivariant Euler characteristics of subspace posets

    Authors: Jesper M. Møller

    Abstract: We compute the (primary) equivariant Euler characteristics of the building for the general linear group over a finite field.

    Submitted 5 February, 2019; v1 submitted 12 January, 2017; originally announced January 2017.

    Comments: 17 pages, revised version

    Report number: CPH-SYM-DNRF92

  126. Some finiteness results for groups of automorphisms of manifolds

    Authors: Alexander Kupers

    Abstract: We prove that in dimensions not equal to 4, 5, or 7, the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses homological stability, embedding calculus and the arithmeticity of mapping class groups. From this we deduce similar results for the homeomorphisms of $R^n$ and… ▽ More

    Submitted 1 September, 2019; v1 submitted 30 December, 2016; originally announced December 2016.

    Comments: 44 pages, 2 figures. To appear in Geometry & Topology. Corrected grant information

    Report number: CPH-SYM-DNRF92 MSC Class: 57S05

    Journal ref: Geom. Topol. 23 (2019) 2277-2333

  127. arXiv:1612.08673  [pdf, other

    math.QA

    Non-commutative coverings spaces

    Authors: Clarisson Rizzie Canlubo

    Abstract: In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings of commutative spaces and coverings of non-commutative tori.

    Submitted 27 December, 2016; originally announced December 2016.

    Comments: 51 pages, 3 figures, first part of my phd thesis

    Report number: CPH-SYM-DNRF92

  128. arXiv:1612.06317  [pdf, other

    math.QA

    Hopf algebroids, Hopf categories and their Galois theories

    Authors: Clarisson Rizzie Canlubo

    Abstract: Hopf algebroids are generalization of Hopf algebras over non-commutative base rings. It consists of a left- and a right-bialgebroid structure related by a map called the antipode. However, if the base ring of a Hopf algebroid is commutative one does not necessarily have a Hopf algebra. Meanwhile, a Hopf category is the categorification of a Hopf algebra. It consists of a category enriched over a b… ▽ More

    Submitted 19 December, 2016; originally announced December 2016.

    Report number: CPH-SYM-DNRF92

  129. arXiv:1612.03732  [pdf, ps, other

    math.AT math.KT

    On exotic equivalences and a theorem of Franke

    Authors: Irakli Patchkoria

    Abstract: Using Franke's methods we construct new examples of exotic equivalences. We show that for any symmetric ring spectrum $R$ whose graded homotopy ring $π_*R$ is concentrated in dimensions divisible by a natural number $N \geq 5$ and has homological dimension at most three, the homotopy category of $R$-modules is equivalent to the derived category of $π_*R$. The Johnson-Wilson spectrum $E(3)$ and the… ▽ More

    Submitted 12 December, 2016; originally announced December 2016.

    Report number: CPH-SYM-DNRF92 MSC Class: 55P42; 18G55; 18E30

  130. arXiv:1612.02694  [pdf, ps, other

    math.AT

    The $v_n$-periodic Goodwillie tower on Wedges and Cofibres

    Authors: Lukas Brantner, Gijs Heuts

    Abstract: We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge $X \vee Y$ of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{cof}(f)$ of a map $f: X \rightarrow Y$. We deduce some consequences for $v_n$-periodic homotopy groups: whereas the Goodwillie tower is finite and converges in periodic homotopy when evaluated on spheres (Arone-Mahowald),… ▽ More

    Submitted 16 May, 2019; v1 submitted 8 December, 2016; originally announced December 2016.

    Comments: 17 pages. Journal version

    Report number: CPH-SYM-DNRF92 MSC Class: 55P65; 55P42; 55Q20; 55Q51

  131. arXiv:1611.08462  [pdf, ps, other

    math.OA math.LO

    Axiomatizability of the stable rank of C*-algebras

    Authors: Ilijas Farah, Mikael Rørdam

    Abstract: We show that the class of C*-algebras with stable rank greater than a given positive integer is axiomatizable in logic of metric structures. As a consequence we show that the stable rank is continuous with respect to forming ultrapowers of C*-algebras, and that stable rank is Kadison--Kastler stable.

    Submitted 16 January, 2017; v1 submitted 25 November, 2016; originally announced November 2016.

    Comments: Minor changes. To appear in Münster J. Math

    Report number: CPH-SYM-DNRF92

  132. The complete classification of unital graph $C^*$-algebras: Geometric and strong

    Authors: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen

    Abstract: We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered $K$-theory. The classification result is geometric in the sense that it establishes that any Morita equivalence between $C^*(E)$ and $C^*(F)$ in this class can be realize… ▽ More

    Submitted 25 August, 2019; v1 submitted 21 November, 2016; originally announced November 2016.

    Comments: This article draws heavily on results and notation developed in arXiv:1602.03709, arXiv:1604.05439 and arXiv:1605.06153, and together with these papers supersedes the results of arXiv:1505.06773, which will not be published. The second version adjusts the proof of decidability in Section 14.2 to the appeared version of [BS18], corrects the statement of Corollary 3.6, and updates references

    Report number: CPH-SYM-DNRF92 and H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS MSC Class: 46L35; 46L80; 46L55; 37B10; 16B99; 46L05

    Journal ref: Duke Math. J. Vol. 170 (2021), no. 11, pp. 2421-2517

  133. Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

    Authors: Toke Meier Carlsen, Søren Eilers, Eduard Ortega, Gunnar Restorff

    Abstract: We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type… ▽ More

    Submitted 28 September, 2018; v1 submitted 31 October, 2016; originally announced October 2016.

    Comments: 25 pages. Minor changes have been made and the list of references has been updated. This is the version that will be published

    Report number: CPH-SYM-DNRF92 MSC Class: 37B10 (Primary); 16S99; 22A33; 37A55; 46L55 (Secondary)

    Journal ref: Journal of Mathematical Analysis and Applications 469 (2019), 1088-1110

  134. arXiv:1610.08392  [pdf, other

    math.CT math.AG math.AT

    The compactness locus of a geometric functor and the formal construction of the Adams isomorphism

    Authors: Beren Sanders

    Abstract: We introduce the compactness locus of a geometric functor between rigidly-compactly generated tensor-triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset of the tensor-triangular spectrum of the target category which, crudely speaking, measures the failure of the functor to satisfy Grothendieck-Neeman duality (o… ▽ More

    Submitted 25 January, 2019; v1 submitted 26 October, 2016; originally announced October 2016.

    Comments: 45 pages. Proof of Proposition 3.2 corrected, major revision to Section 7 (now containing stronger results), minor expository improvements elsewhere

    Report number: CPH-SYM-DNRF92

    Journal ref: Journal of Topology 12 (2019) 287-327

  135. arXiv:1610.08387  [pdf, ps, other

    math.CT math.AT

    A note on triangulated monads and categories of module spectra

    Authors: Ivo Dell'Ambrogio, Beren Sanders

    Abstract: Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other triangulated adjunction realizing this monad is 'essentially monadic', i.e. becomes monadic after performing the two evident necessary operations of taking the Verdier quotient by the kernel of the right adjoint and idempot… ▽ More

    Submitted 1 August, 2018; v1 submitted 26 October, 2016; originally announced October 2016.

    Comments: 5 pages

    Report number: CPH-SYM-DNRF92

    Journal ref: C. R. Math. Acad. Sci. Paris 356 (2018) 839-842

  136. Equivariant Kirchberg-Phillips-type absorption for amenable group actions

    Authors: Gabor Szabo

    Abstract: We show an equivariant Kirchberg-Phillips-type absorption theorem for pointwise outer actions of discrete amenable groups on Kirchberg algebras with respect to natural model actions on the Cuntz algebras $\mathcal{O}_\infty$ and $\mathcal{O}_2$. This generalizes results known for finite groups and poly-$\mathbb{Z}$ groups. The model actions are shown to be determined, up to strong cocycle conjugac… ▽ More

    Submitted 11 January, 2018; v1 submitted 19 October, 2016; originally announced October 2016.

    Comments: v3 42 pages; this version has been accepted for publication in Communications in Mathematical Physics

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55 (primary); 46L05; 19K35 (secondary)

    Journal ref: Comm. Math. Phys. 361 (2018), no. 3, pp. 1115--1154

  137. Filtered K-theory for graph algebras

    Authors: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen

    Abstract: We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge invariant filtered $K$-theory for graph $C^*$-algebras. We apply this to verify the Abrams-Tomforde conjecture for a large class of finite graphs.

    Submitted 7 October, 2016; originally announced October 2016.

    Comments: 16 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 16B99; 46L05; 46L55

    Journal ref: 2016 MATRIX annals, pp. 229-249, MATRIX Book Ser., 1, Springer, Cham, 2018

  138. arXiv:1609.07635  [pdf, ps, other

    math.GR math.FA

    Amenable groups of finite cohomological dimension and the zero divisor conjecture

    Authors: Dieter Degrijse

    Abstract: We prove that every amenable group of cohomological dimension two whose integral group ring is a domain is solvable and investigate certain homological finiteness properties of groups that satisfy the analytic zero divisor conjecture and act on an acyclic CW-complex with amenable stabilisers.

    Submitted 24 September, 2016; originally announced September 2016.

    Comments: 12 pages

    Report number: CPH-SYM-DNRF92

  139. arXiv:1609.05086  [pdf, ps, other

    math.OA math.GR

    Non-inner amenability of the Thompson groups T and V

    Authors: Uffe Haagerup, Kristian Knudsen Olesen

    Abstract: In this paper we prove that the Thompson groups $T$ and $V$ are not inner amenable. In particular, their group von Neumann algebras do not have property $Γ$. Moreover, we prove that if the reduced group $C^\ast$-algebra of $T$ is simple, then the Thompson group $F$ is non-amenable. Furthermore, we give a few new equivalent characterizations of amenability of $F$.

    Submitted 16 September, 2016; originally announced September 2016.

    Comments: 13 pages

    Report number: CPH-SYM-DNRF92

  140. arXiv:1608.08140  [pdf, other

    math.AT math.QA

    Free loop spaces and dihedral homology

    Authors: Massimiliano Ungheretti

    Abstract: We prove an $O(2)$-equivariant version of the Jones isomorphism relating the Borel $O(2)$-equivariant cohomology of the free loop space to the dihedral homology of the cochain algebra. We discuss polynomial forms and a variation of the de Rham isomorphism and use these to do a computation for the 2-sphere.

    Submitted 29 August, 2016; originally announced August 2016.

    Comments: 27 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 55P50; 55P35 (primary); 16E40; 19D55 (secondary)

  141. arXiv:1608.02063  [pdf, ps, other

    math.AT

    A short proof of telescopic Tate vanishing

    Authors: Dustin Clausen, Akhil Mathew

    Abstract: We give a short proof of a theorem of Kuhn that Tate constructions for finite group actions vanish in telescopically localized stable homotopy theory. In particular, we observe that Kuhn's theorem is equivalent to the statement that the transfer $BC_{p+} \to S^0$ admits a section after telescopic localization, which in turn follows from the Kahn-Priddy theorem.

    Submitted 4 January, 2017; v1 submitted 6 August, 2016; originally announced August 2016.

    Comments: 4 pages. Revised version adds additional references and remarks. To appear in Proceedings of the AMS

    Report number: CPH-SYM-DNRF92

  142. arXiv:1608.01290  [pdf, ps, other

    math.AT math.AG math.QA

    Linear Batalin-Vilkovisky quantization as a functor of $\infty$-categories

    Authors: Owen Gwilliam, Rune Haugseng

    Abstract: We study linear Batalin-Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, we implement this construction as a symmetric monoidal functor of $\infty$-categories. We also show that this construction has a number of pleasant properties: It has a natural extension to derived algebraic geo… ▽ More

    Submitted 27 February, 2020; v1 submitted 3 August, 2016; originally announced August 2016.

    Comments: 50 pages, final version

    Report number: CPH-SYM-DNRF92

  143. arXiv:1608.00499  [pdf, other

    math.GR math.AT math.RT

    Endotrivial modules for finite groups via homotopy theory

    Authors: Jesper Grodal

    Abstract: Classifying endotrivial kG-modules, i.e., elements of the Picard group of the stable module category for an arbitrary finite group G, has been a long-running quest. By deep work of Dade, Alperin, Carlson, Thevenaz, and others, it has been reduced to understanding the subgroup consisting of modular representations that split as the trivial module k direct sum a projective module when restricted to… ▽ More

    Submitted 14 January, 2022; v1 submitted 1 August, 2016; originally announced August 2016.

    Comments: v3: Final version, revised following referee reports. To appear in J. Amer. Math. Soc

    Report number: CPH-SYM-DNRF92, CPH-GEOTOP-DNRF151 MSC Class: 20C20 (20J06; 18G10; 20J99)

    Journal ref: J. Amer. Math. Soc. 36 (2023) no. 1, 177-250

  144. Symmetric products and subgroup lattices

    Authors: Markus Hausmann

    Abstract: Let G be a finite group. We show that the rational homotopy groups of symmetric products of the G-equivariant sphere spectrum are naturally isomorphic to the rational homology groups of certain subcomplexes of the subgroup lattice of G.

    Submitted 4 May, 2018; v1 submitted 26 July, 2016; originally announced July 2016.

    Comments: final published version

    Report number: CPH-SYM-DNRF92

    Journal ref: Geom. Topol. 22 (2018) 1547-1591

  145. arXiv:1607.07143  [pdf, ps, other

    math.KT math.FA math.OA

    Boundaries, spectral triples and K-homology

    Authors: Iain Forsyth, Magnus Goffeng, Bram Mesland, Adam Rennie

    Abstract: This paper extends the notion of a spectral triple to a relative spectral triple, an unbounded analogue of a relative Fredholm module for an ideal $J\triangleleft A$. Examples include manifolds with boundary, manifolds with conical singularities, dimension drop algebras, $θ$-deformations and Cuntz-Pimsner algebras of vector bundles. The bounded transform of a relative spectral triple is a relati… ▽ More

    Submitted 24 July, 2016; originally announced July 2016.

    Report number: CPH-SYM-DNRF92

    Journal ref: J. Noncommut. Geom. 13 (2) (2019) 407--472

  146. arXiv:1607.04486  [pdf, ps, other

    math.RT

    A variant of Harish-Chandra functors

    Authors: Tyrone Crisp, Ehud Meir, Uri Onn

    Abstract: Harish-Chandra induction and restriction functors play a key role in the representation theory of reductive groups over finite fields. In this paper, extending earlier work of Dat, we introduce and study generalisations of these functors which apply to a wide range of finite and profinite groups, typical examples being compact open subgroups of reductive groups over non-archimedean local fields. W… ▽ More

    Submitted 15 July, 2016; originally announced July 2016.

    Comments: 43 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 22E50 (20G25; 20C33; 20C15; 20C07)

  147. Modular characteristic classes for representations over finite fields

    Authors: Anssi Lahtinen, David Sprehn

    Abstract: The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial elements is exponential in $n$. In this paper, we introduce a new system of characteristic classes for representations over finite fields, and use it to constru… ▽ More

    Submitted 17 October, 2017; v1 submitted 4 July, 2016; originally announced July 2016.

    Comments: Accepted to the Advances in Mathematics

    Report number: CPH-SYM-DNRF92 MSC Class: 20J06; 20C20

    Journal ref: Advances in Mathematics 323 (2018), pp. 1-37

  148. Global model structures for $*$-modules

    Authors: Benjamin Böhme

    Abstract: We extend Schwede's work on the unstable global homotopy theory of orthogonal spaces and $\mathcal{L}$-spaces to the category of $*$-modules (i.e., unstable $S$-modules). We prove a theorem which transports model structures and their properties from $\mathcal{L}$-spaces to $*$-modules and show that the resulting global model structure for $*$-modules is monoidally Quillen equivalent to that of ort… ▽ More

    Submitted 28 February, 2018; v1 submitted 1 July, 2016; originally announced July 2016.

    Comments: 22 pages. Small changes to the class of cofibrations, due to changes in the main reference, arXiv:1711.06019. Improved exposition and minor revisions in response to a referee report

    Report number: CPH-SYM-DNRF92 MSC Class: 55P91; 18G55

    Journal ref: Homology Homotopy Appl. 21 (2019), no. 2, 213-230

  149. Characterizations of locally finite actions of groups on sets

    Authors: Eduardo Scarparo

    Abstract: We show that an action of a group on a set $X$ is locally finite if and only if $X$ is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.

    Submitted 4 January, 2017; v1 submitted 27 June, 2016; originally announced June 2016.

    Comments: 4 pages. Minor clarification made in the paragraph after Remark 2.6. To appear in the Glasgow Mathematical Journal

    Report number: CPH-SYM-DNRF92

    Journal ref: Glasgow Mathematical Journal, Volume 60, Issue 2 May 2018 , pp. 285-288

  150. arXiv:1606.06716  [pdf, ps, other

    math.AG

    A vanishing result for tautological classes on the moduli of K3 surfaces

    Authors: Dan Petersen

    Abstract: Looijenga's vanishing theorem on the moduli space of curves $M_g$ says that the tautological ring vanishes above degree $g-2$. We prove an analogous result for the tautological cohomology ring of the moduli space of K3 surfaces.

    Submitted 16 February, 2017; v1 submitted 21 June, 2016; originally announced June 2016.

    Comments: 3 pages. v2: Reference added. To appear in Amer J Math

    Report number: CPH-SYM-DNRF92

    Journal ref: Am. J. Math. 141, No. 3, 733-736 (2019)

  151. arXiv:1606.05449  [pdf, ps, other

    math.DS math.KT math.OA

    Wieler solenoids, Cuntz-Pimsner algebras and K-theory

    Authors: Robin J. Deeley, Magnus Goffeng, Bram Mesland, Michael F. Whittaker

    Abstract: We study irreducible Smale spaces with totally disconnected stable sets and their associated $K$-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows three converging tracks: one dynamical, one operator algebraic and one $K$-theoretic. Using Wieler's Theorem, we characterize the unstable set of a finite set of… ▽ More

    Submitted 17 June, 2016; originally announced June 2016.

    Report number: CPH-SYM-DNRF92, SOAR-GMJT-01

    Journal ref: Ergodic Theory and Dynamical Systems 38 (2018), 2942-2988

  152. arXiv:1606.03826  [pdf, ps, other

    math.AT math.CT

    Two models for the homotopy theory of $\infty$-operads

    Authors: Hongyi Chu, Rune Haugseng, Gijs Heuts

    Abstract: We compare two models for $\infty$-operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison results already in the literature, this implies that all known models for $\infty$-operads are equivalent - for instance, it follows that the homotopy theory of Lurie's $\infty$-operads is equivalent to that of dendroida… ▽ More

    Submitted 31 October, 2020; v1 submitted 13 June, 2016; originally announced June 2016.

    Comments: 16 pages, v2: accepted version

    Report number: CPH-SYM-DNRF92

    Journal ref: Journal of Topology 11(4) (2018) 856-872

  153. arXiv:1606.03328  [pdf, ps, other

    math.KT math.AT

    Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes

    Authors: Dustin Clausen, Akhil Mathew, Niko Naumann, Justin Noel

    Abstract: Let $A \to B$ be a $G$-Galois extension of rings, or more generally of $\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in algebraic $K$-theory asks how close the map $K(A) \to K(B)^{hG}$ is to being an equivalence, i.e., how close algebraic $K$-theory is to satisfying Galois descent. An elementary argument with the transfer shows that this equivalence is true rationally i… ▽ More

    Submitted 22 November, 2017; v1 submitted 10 June, 2016; originally announced June 2016.

    Comments: 46 pages. With an appendix by Lennart Meier, Niko Naumann, and Justin Noel. Revised version, to appear in Journal of the European Mathematical Society

    Report number: CPH-SYM-DNRF92

    Journal ref: J. Eur. Math. Soc. (JEMS) 22 (2020), no. 4, 1149-1200

  154. Fixed Point Algebras for Easy Quantum Groups

    Authors: Olivier Gabriel, Moritz Weber

    Abstract: Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their $K$-groups. Building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the $K$-groups of their fixed p… ▽ More

    Submitted 1 October, 2016; v1 submitted 2 June, 2016; originally announced June 2016.

    Report number: CPH-SYM-DNRF92 MSC Class: 46L80; 19K99; 81R50

    Journal ref: SIGMA 12 (2016), 097, 21 pages

  155. arXiv:1606.00413  [pdf, ps, other

    math.SP math.FA math.OA

    Nonclassical spectral asymptotics and Dixmier traces: From circles to contact manifolds

    Authors: Heiko Gimperlein, Magnus Goffeng

    Abstract: We consider the spectral behavior and noncommutative geometry of commutators $[P,f]$, where $P$ is an operator of order $0$ with geometric origin and $f$ a multiplication operator by a function. When $f$ is Hölder continuous, the spectral asymptotics is governed by singularities. We study precise spectral asymptotics through the computation of Dixmier traces; such computations have only been consi… ▽ More

    Submitted 1 June, 2016; originally announced June 2016.

    Comments: 40 pages

    Report number: SOAR-GMJT-01, CPH-SYM-DNRF92

    Journal ref: Forum of Mathematics, Sigma 5 (2017), e3

  156. arXiv:1605.06909  [pdf, ps, other

    math.OA math.FA math.GR

    Unitarizability, Maurey--Nikishin factorization, and Polish groups of finite type

    Authors: Hiroshi Ando, Yasumichi Matsuzawa, Andreas Thom, Asger Törnquist

    Abstract: Let $Γ$ be a countable discrete group, and let $π\colon Γ\to {\rm{GL}}(H)$ be a representation of $Γ$ by invertible operators on a separable Hilbert space $H$. We show that the semidirect product group $G=H\rtimes_πΓ$ is SIN ($G$ admits a two-sided invariant metric compatible with its topology) and unitarily representable ($G$ embeds into the unitary group $\mathcal{U}(\ell^2(\mathbb N))$), if and… ▽ More

    Submitted 12 September, 2017; v1 submitted 23 May, 2016; originally announced May 2016.

    Comments: 27 pages v2 minor changes: corrected the hypothesis in Corollary 3.16 and first few lines of the proof of Lemma 3.7

    Report number: CPH-SYM-DNRF92

  157. arXiv:1605.06508  [pdf, other

    math.KT math.AT math.GR math.GT

    The rational stable homology of mapping class groups of universal nil-manifolds

    Authors: Markus Szymik

    Abstract: We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers and the automorphism groups of free groups, and we employ functor homology to reduce to the abelian case. As an application, we also compute the rational stable homology of the outer automorphism groups and of the mapping… ▽ More

    Submitted 26 April, 2018; v1 submitted 20 May, 2016; originally announced May 2016.

    Comments: 25 pages, will appear at Annales de l'Institut Fourier

    Report number: CPH-SYM-DNRF92

    Journal ref: Ann. Inst. Fourier 69 (2019) 783-803

  158. arXiv:1605.01202  [pdf, ps, other

    math.OA

    A dynamical characterization of diagonal preserving $*$-isomorphisms of graph $C^*$-algebras

    Authors: Sara E. Arklint, Søren Eilers, Efren Ruiz

    Abstract: We characterize when there exists a diagonal preserving $*$-isomorphism between two graph $C^*$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of "orbit equivalence" between the boundary path spaces of the directed graphs $E$ and $F$ and show that this is a necessary and sufficient condition for the existence of a diagonal preserving $*$-isomorph… ▽ More

    Submitted 4 May, 2016; originally announced May 2016.

    Report number: CPH-SYM-DNRF92. This work is also part of the project supported by the grant H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS MSC Class: Primary: 46L55; Secondary: 46L35; 37B10

  159. arXiv:1605.00845  [pdf, ps, other

    math.AT math.GR

    Stable finiteness properties of infinite discrete groups

    Authors: Noé Bárcenas, Dieter Degrijse, Irakli Patchkoria

    Abstract: Let $G$ be an infinite discrete group. A classifying space for proper actions of $G$ is a proper $G$-CW-complex $X$ such that the fixed point sets $X^H$ are contractible for all finite subgroups $H$ of $G$. In this paper we consider the stable analogue of the classifying space for proper actions in the category of proper $G$-spectra and study its finiteness properties. We investigate when $G$ admi… ▽ More

    Submitted 3 May, 2016; originally announced May 2016.

    Comments: 25 pages

    Report number: CPH-SYM-DNRF92

  160. arXiv:1604.08774  [pdf, ps, other

    math.OA math.GR

    Just-infinite C*-algebras

    Authors: Rostislav Grigorchuk, Magdalena Musat, Mikael Rørdam

    Abstract: By analogy with the well-established notions of just-infinite groups and just-infinite (abstract) algebras, we initiate a systematic study of just-infinite C*-algebras, i.e., infinite dimensional C*-algebras for which all proper quotients are finite dimensional. We give a classification of such C*-algebras in terms of their primitive ideal space that leads to a trichotomy. We show that just-infini… ▽ More

    Submitted 3 April, 2017; v1 submitted 29 April, 2016; originally announced April 2016.

    Comments: 36 pages. To appear in Commentarii Math. Helvetici

    Report number: CPH-SYM-DNRF92 MSC Class: 46L05; 37A55; 20C07; 46L36

  161. arXiv:1604.08480  [pdf, ps, other

    math.AT math.CT

    On the equivalence between $Θ_{n}$-spaces and iterated Segal spaces

    Authors: Rune Haugseng

    Abstract: We give a new proof of the equivalence between two of the main models for $(\infty,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the $Θ_{n}$-spaces of Rezk, by proving that these are algebras for the same monad on the $\infty$-category of $n$-globular spaces. The proof works for a broad class of $\infty$-categories that includes all $\infty$-topoi.

    Submitted 31 October, 2020; v1 submitted 28 April, 2016; originally announced April 2016.

    Comments: 15 pages, v2: accepted version

    Report number: CPH-SYM-DNRF92 MSC Class: 18D05; 55U40

    Journal ref: Proceedings of the AMS 146(4) (2018) 1401-1415

  162. arXiv:1604.08478  [pdf, other

    math.GR math.AT

    Classifying spaces for families of subgroups for systolic groups

    Authors: Damian Osajda, Tomasz Prytuła

    Abstract: We determine the large scale geometry of the minimal displacement set of a hyperbolic isometry of a systolic complex. As a consequence, we describe the centraliser of such an isometry in a systolic group. Using these results, we construct a low-dimensional classifying space for the family of virtually cyclic subgroups of a group acting properly on a systolic complex. Its dimension coincides with t… ▽ More

    Submitted 15 January, 2018; v1 submitted 28 April, 2016; originally announced April 2016.

    Comments: Second version: 60 pages, 16 figures, new proof of Proposition 4.6, minor corrections in proofs in Sections 4 and 6, this version contains more (expository) material than the version accepted by Groups, Geometry and Dynamics

    Report number: CPH-SYM-DNRF92 MSC Class: 20F65; 55R35 (Primary); 20F67; 20F06 (Secondary)

  163. arXiv:1604.05684  [pdf, ps, other

    math.OA

    Structural properties of close II$_1$ factors

    Authors: Jan Cameron, Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart White, Alan D. Wiggins

    Abstract: We show that a number of key structural properties transfer between sufficiently close II$_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $Γ$. We also examine II$_1$ factors close to tensor product factors, showing that such factors also factorise as a tensor product in a fashion close to the original.

    Submitted 31 May, 2016; v1 submitted 19 April, 2016; originally announced April 2016.

    Comments: Minor typos corrected. Munster J. Math., to appear. 16 pages, section 2 contains material from arXiv:1209.4116v2 which was removed from the final published version (v3)

    Report number: CPH-SYM-00; SOAR-GMJT-01 MSC Class: 46L10

  164. Geometric classification of graph $C^*$-algebras over finite graphs

    Authors: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen

    Abstract: We address the classification problem for graph $C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph $C^*$-algebras may come with uncountable ideal structures. We find that in this generality, s… ▽ More

    Submitted 1 November, 2016; v1 submitted 19 April, 2016; originally announced April 2016.

    Comments: Corrected typos, corrected minor errors in statements and proofs of some results, and added Lemma 6.6

    Report number: CPH-SYM-DNRF92. This work is also part of the project supported by the grant H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS MSC Class: 46L35; 46L80; 46L55; 37B10

    Journal ref: Canad. J. Math. 70 (2018), no. 2, 294-353

  165. arXiv:1604.03085  [pdf, ps, other

    math.OA

    Hereditary $C^*$-subalgebras of graph $C^*$-algebras

    Authors: Sara E. Arklint, James Gabe, Efren Ruiz

    Abstract: We show that a $C^*$-algebra $\mathfrak{A}$ which is stably isomorphic to a unital graph $C^*$-algebra, is isomorphic to a graph $C^*$-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary $C^*$-subalgebra of a unital real rank zero graph $C^*$-algebra is isomorphic to a graph $C^*$-algebra. Furthermore, if a $C^*$-algebra $\mathfrak{A}$ admits an appr… ▽ More

    Submitted 31 January, 2017; v1 submitted 11 April, 2016; originally announced April 2016.

    Comments: 23 pages. Ver 2: 24 pages, minor changes to introduction, bibliography updated

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55

  166. arXiv:1603.09641  [pdf, other

    math.RT math.AC math.AG math.AT

    Spectral sequences for Hochschild cohomology and graded centers of derived categories

    Authors: Frank Neumann, Markus Szymik

    Abstract: The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the failure of the characteristic homomorphism to be injective or surjective, in general. To illustra… ▽ More

    Submitted 5 May, 2017; v1 submitted 31 March, 2016; originally announced March 2016.

    Comments: 29 pages, 1 figure, to appear in Selecta Mathematica

    Report number: CPH-SYM-DNRF92

    Journal ref: Selecta Math. 23 (2017) 1997-2018

  167. arXiv:1603.08797  [pdf, ps, other

    math.RT math.OA

    A Second Adjoint Theorem for SL(2,R)

    Authors: Tyrone Crisp, Nigel Higson

    Abstract: We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).

    Submitted 29 March, 2016; originally announced March 2016.

    Comments: 38 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 22E45

  168. arXiv:1603.04681  [pdf, ps, other

    math.AT math.KT

    The derived category of complex periodic K-theory localized at an odd prime

    Authors: Irakli Patchkoria

    Abstract: We prove that for an odd prime $p$, the derived category $\mathcal{D}(KU_{(p)})$ of the $p$-local complex periodic $K$-theory spectrum $KU_{(p)}$ is triangulated equivalent to the derived category of its homotopy ring $π_*KU_{(p)}$. This implies that if $p$ is an odd prime, the triangulated category $\mathcal{D}(KU_{(p)})$ is algebraic.

    Submitted 15 March, 2016; originally announced March 2016.

    Report number: CPH-SYM-DNRF92 MSC Class: 55P42; 18G55; 18E30

  169. arXiv:1603.01829  [pdf, ps, other

    math.GR math.OA

    Exactness of locally compact groups

    Authors: Jacek Brodzki, Chris Cave, Kang Li

    Abstract: We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.

    Submitted 22 March, 2017; v1 submitted 6 March, 2016; originally announced March 2016.

    Comments: 18 pages, to appear in Adv. Math

    Report number: CPH-SYM-DNRF92

  170. arXiv:1603.01166  [pdf, ps, other

    math.OA math.KT

    Regularity of Villadsen algebras and characters on their central sequence algebras

    Authors: Martin S. Christensen

    Abstract: We show that if A is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of A does not admit characters. Additionally, in a joint appendix with Joan Bosa, we show that the Villadsen algebra of the second type with infinite stable rank… ▽ More

    Submitted 3 May, 2017; v1 submitted 3 March, 2016; originally announced March 2016.

    Comments: 24 pages. Math. Scand., to appear

    Report number: CPH-SYM-DNRF92 MSC Class: 46L05; 46L35 46L80

    Journal ref: Math. Scand. 123 (2018) 121-141; Appendix: Math. Scand. 123 (2018) 142-146

  171. arXiv:1603.01137  [pdf, other

    math.AT math.AG math.CO math.GT

    A spectral sequence for stratified spaces and configuration spaces of points

    Authors: Dan Petersen

    Abstract: We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology groups of the poset of strata. Several familiar spectral sequences arise as special cases. The construction is sheaf-theoretic and works both for topological s… ▽ More

    Submitted 30 August, 2016; v1 submitted 3 March, 2016; originally announced March 2016.

    Comments: 23 pages. v2: Several minor improvements and corrections, the arguments in Subsection 3.2 have been fleshed out. Final version, to appear in Geometry & Topology

    Report number: CPH-SYM-DNRF92 MSC Class: 55R80; 14N20; 58A35; 55N30; 18G10

    Journal ref: Geom. Topol. 21 (2017) 2527-2555

  172. Free loop space and the cyclic bar construction

    Authors: Massimiliano Ungheretti

    Abstract: Using the $E_\infty-$structure on singular cochains, we construct a homotopy coherent map from the cyclic bar construction of the differential graded algebra of cochains on a space to a model for the cochains on its free loop space. This fills a gap in the paper "Cyclic homology and equivariant homology" by John D.S. Jones.

    Submitted 29 August, 2016; v1 submitted 29 February, 2016; originally announced February 2016.

    Comments: 9 pages, minor changes

    Report number: CPH-SYM-DNRF92 MSC Class: 55P50; 55P35 (Primary); 16E40; 19D55; 55S20 (Secondary)

  173. arXiv:1602.04354  [pdf, ps, other

    math.GR math.AT math.GT

    Dimension invariants of outer automorphism groups

    Authors: Dieter Degrijse, Juan Souto

    Abstract: The geometric dimension for proper actions $\underline{\mathrm{gd}}(G)$ of a group $G$ is the minimal dimension of a classifying space for proper actions $\underline{E}G$. We construct for every integer $r\geq 1$, an example of a virtually torsion-free Gromov-hyperbolic group $G$ such that for every group $Γ$ which contains $G$ as a finite index normal subgroup, the virtual cohomological dimension… ▽ More

    Submitted 13 February, 2016; originally announced February 2016.

    Comments: 24 pages

    Report number: CPH-SYM-DNRF92

  174. arXiv:1602.04131  [pdf, other

    math.AT math.MG

    On homotopy types of Euclidean Rips complexes

    Authors: Michal Adamaszek, Florian Frick, Adrien Vakili

    Abstract: The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We prove that for X in the Euclidean 3-space R^3 the natural projection map from the Rips complex of X to its shadow in R^3 induces a surjection on fundamental groups. This partially answers a question of Chambers, de Silva… ▽ More

    Submitted 12 February, 2016; originally announced February 2016.

    Report number: CPH-SYM-DNRF92

    Journal ref: Discrete & Computational Geometry 58(3):526-542 (2017)

  175. Invariance of the Cuntz splice

    Authors: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen

    Abstract: We show that the Cuntz splice induces stably isomorphic graph $C^*$-algebras.

    Submitted 12 February, 2016; v1 submitted 11 February, 2016; originally announced February 2016.

    Comments: Our arguments to prove invariance of the Cuntz splice for unital graph C*-algebras in arXiv:1505.06773 applied with only minor changes in the general case. Since most of the results of that preprint have since been superseded by other forthcoming work, we do not intend to publish it, whereas this work is intended for publication. arXiv admin note: substantial text overlap with arXiv:1505.06773

    Report number: CPH-SYM-DNRF92 MSC Class: 46L35; 46L80; 46L55; 37B10

    Journal ref: Math. Ann., Vol. 369 (2017), no. 3-4, pp. 1061-1080

  176. arXiv:1602.01533  [pdf, ps, other

    math.OA math.DS

    Reduced twisted crossed products over C*-simple groups

    Authors: Rasmus Sylvester Bryder, Matthew Kennedy

    Abstract: We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In par… ▽ More

    Submitted 3 February, 2016; originally announced February 2016.

    Comments: 16 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L35; 16S35; 43A65

  177. arXiv:1602.01274  [pdf, ps, other

    math.AT math.CT

    Left fibrations and homotopy colimits II

    Authors: Gijs Heuts, Ieke Moerdijk

    Abstract: For a small simplicial category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the homotopy-coherent nerve of A provides a left Quillen equivalence between the projective model structure on the former category and the covariant model structure on the latter. We compare this Quillen equivalence to the straightening… ▽ More

    Submitted 3 February, 2016; originally announced February 2016.

    Report number: CPH-SYM-DNRF92

  178. arXiv:1601.05048  [pdf, ps, other

    math.QA math-ph math.SG

    Classification of Group Actions Extended to Symplectic Deformation Quantizations

    Authors: Niek de Kleijn

    Abstract: Consider a group $Γ$ acting on a formal (Fedosov) deformation quantization $\mathbb{A}_\hbar(M)$ of a symplectic manifold $(M,ω)$. This canonically induces an action of $Γ$ by symplectomorphisms on $M$. We examine the reverse problem of extending group actions by symplectomorphisms to the deformation quantization. To do this we first define a notion of extension that does not impose restrictions o… ▽ More

    Submitted 30 May, 2017; v1 submitted 19 January, 2016; originally announced January 2016.

    Comments: 28 pages, comments welcome; Corrected typos, added references and corrected an error in definition 5.7

    Report number: CPH-SYM-DNRF92

  179. arXiv:1601.04566  [pdf, ps, other

    math.GR math.AT

    Automorphisms of fusion systems of finite simple groups of Lie type

    Authors: Carles Broto, Jesper M. Møller, Bob Oliver

    Abstract: For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex, but can always be reduced to a case… ▽ More

    Submitted 18 January, 2016; originally announced January 2016.

    Comments: 99 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 20G40; 55P10

  180. arXiv:1512.08099  [pdf, other

    math.CO

    Equivariant Euler characteristics of partition posets

    Authors: Jesper M. Moller

    Abstract: We compute all the equivariant Euler characteristics of the $Σ_n$-poset of partitions of the $n$ element set.

    Submitted 26 December, 2015; originally announced December 2015.

    Comments: 10 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 05E18

  181. arXiv:1512.07277  [pdf, other

    math.OA

    Semiprojectivity and properly infinite projections in graph C*-algebras

    Authors: Søren Eilers, Takeshi Katsura

    Abstract: We give a complete description of which unital graph C*-algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such C*-algebras.

    Submitted 22 December, 2015; originally announced December 2015.

    Report number: CPH-SYM-DNRF92

  182. Flow Equivalence of G-SFTs

    Authors: Mike Boyle, Toke Meier Carlsen, Søren Eilers

    Abstract: In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G. For a special case of two irreducible components with G$=\mathbb Z_2$, we… ▽ More

    Submitted 26 August, 2019; v1 submitted 16 December, 2015; originally announced December 2015.

    Comments: The paper has been augmented considerably and the second version is now 81 pages long. This version has been accepted for publication in Transactions of the American Mathematical Society

    Report number: CPH-SYM-DNRF92

    Journal ref: Trans. Amer. Math. Soc. 373 (2020), 2591-2657

  183. arXiv:1512.04979  [pdf, ps, other

    math.FA math-ph math.OA

    Commutator inequalities via Schur products

    Authors: Erik Christensen

    Abstract: For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| \leq A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The proofs take place in a space of infinite matrices with operator entries, and in this setting it is possible to approximate the matrix associated to [g(D),… ▽ More

    Submitted 15 December, 2015; originally announced December 2015.

    Comments: 16 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 46L55; 47D06; 58B34; 81S05

  184. arXiv:1512.03455  [pdf, ps, other

    math.KT math.DS math.OA math.QA

    Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension

    Authors: Magnus Goffeng, Bram Mesland, Adam Rennie

    Abstract: We show how the fine structure in shift-tail equivalence, appearing in the noncommutative geometry of Cuntz-Krieger algebras developed by the first two authors, has an analogue in a wide range of other Cuntz-Pimsner algebras. To illustrate this structure, and where it appears, we produce an unbounded representative of the defining extension of the Cuntz-Pimsner algebra constructed from a finitely… ▽ More

    Submitted 7 August, 2016; v1 submitted 10 December, 2015; originally announced December 2015.

    Comments: 30 pages

    Report number: CPH-SYM-DNRF92

    Journal ref: Ergodic Th. Dynam. Sys. 38 (4) (2018), 1389--1421

  185. arXiv:1511.06332  [pdf, ps, other

    math.OA math.CT math.QA

    A few remarks on the tube algebra of a monoidal category

    Authors: Sergey Neshveyev, Makoto Yamashita

    Abstract: We prove two results on the tube algebras of rigid C$^*$-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group $G$ is a full corner of the Drinfeld double of $G$. As an application we obtain some information on the structure of the tube algebras of the Temperley-Lieb categories $TL(d)$ for $d>2$. The second result is that the tube algebras… ▽ More

    Submitted 12 March, 2018; v1 submitted 19 November, 2015; originally announced November 2015.

    Comments: 17 pages; v4: minor changes and change of section numbering to the published version, to appear in Proc. Edinb. Math. Soc.; v3: description of the topology on the primitive spectrum of the tube algebra of a Temperley-Lieb category (d>2), a few remarks and minor fixes; v2: rewritten last section

    Report number: CPH-SYM-DNRF92 MSC Class: Primary: 81R15; Secondary: 18D10; 46L89

    Journal ref: Proc. Edinb. Math. Soc. (2) 61 (2018), no. 3, 735-758

  186. arXiv:1511.05793  [pdf, ps, other

    math.RT

    Cusp forms for reductive symmetric spaces of split rank one

    Authors: Erik P. van den Ban, Job J. Kuit

    Abstract: For reductive symmetric spaces G/H of split rank one we identify a class of minimal parabolic subgroups for which certain cuspidal integrals of Harish-Chandra - Schwartz functions are absolutely convergent. Using these integrals we introduce a notion of cusp forms and investigate its relation with representations of the discrete series for G/H.

    Submitted 18 November, 2015; originally announced November 2015.

    Comments: 76 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 22E30; 22E45

  187. arXiv:1511.03526  [pdf, ps, other

    math.AT math.AC math.AG math.CT

    Local duality in algebra and topology

    Authors: Tobias Barthel, Drew Heard, Gabriel Valenzuela

    Abstract: The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts. For any stable $\infty$-category $\mathcal{C}$ together with a collection of compact objects $\mathcal{K} \subset \mathcal{C}$ we construct local cohomology and local homology functors satisfying an abstract version of local duality. When spe… ▽ More

    Submitted 31 July, 2018; v1 submitted 11 November, 2015; originally announced November 2015.

    Comments: Significantly revised version to appear in Advances in Mathematics. Section 6 has been removed, and an expanded version will appear in a separate paper

    Report number: CPH-SYM-DNRF92 MSC Class: 55P60; 13D45; 14B15; 55U35

  188. Flow equivalence of sofic shifts

    Authors: Mike Boyle, Toke Meier Carlsen, Søren Eilers

    Abstract: We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending flow equivalences of subshifts to flow equivalent irreducible shifts of finite type which contain them. (2) The classification of certain constant to one map… ▽ More

    Submitted 12 November, 2015; v1 submitted 11 November, 2015; originally announced November 2015.

    Comments: 30 pages

    Report number: CPH-SYM-DNRF92

    Journal ref: Isr. J. Math. (2018) 225: 111

  189. Flow equivalence and isotopy for subshifts

    Authors: Mike Boyle, Toke Meier Carlsen, Søren Eilers

    Abstract: We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map is not always an isotopy, but that this always is the case for suspension flows of irreducible shifts of finite type. We also provide a version of the fundamen… ▽ More

    Submitted 24 April, 2017; v1 submitted 11 November, 2015; originally announced November 2015.

    Comments: 25 pages. There are various small changes, and also a correction to a misstatement of Theorem 3.1(b) (Theorem 3.3(b) in version 1 and 2). The numbering of theorems, definitions, etc. have been changed such that it agrees with the published version

    Report number: CPH-SYM-DNRF92

    Journal ref: Dyn. Syst. 32 (2017), no. 3, 305-325

  190. Homological stability for automorphism groups of RAAGs

    Authors: Giovanni Gandini, Nathalie Wahl

    Abstract: We show that the homology of the automorphism group of a right-angled Artin group stabilizes under taking products with any right-angled Artin group.

    Submitted 16 September, 2016; v1 submitted 22 October, 2015; originally announced October 2015.

    Comments: final version

    Report number: CPH-SYM-DNRF92 MSC Class: 20F65; 20F28

    Journal ref: Algebr. Geom. Topol. 16 (2016) 2421-2441

  191. arXiv:1510.03304  [pdf, ps, other

    math.AT math.CT

    Goodwillie approximations to higher categories

    Authors: Gijs Heuts

    Abstract: We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More generally, we construct such a tower for a large class of infinity-categories C. We classify such Goodwillie towers in terms of the derivatives of the identity func… ▽ More

    Submitted 25 July, 2018; v1 submitted 12 October, 2015; originally announced October 2015.

    Comments: Version 4: final version to appear in Memoirs of the AMS. Version 3: improved and expanded the exposition, added Section 7.4 on coalgebras with Tate diagonals as a model for homotopy types. Version 2: changed the introduction and added the example of truncated spaces

    Report number: CPH-SYM-DNRF92

  192. On quasi-classical limits of DQ-algebroids

    Authors: Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan

    Abstract: We determine the additional structure which arises on the classical limit of a DQ-algebroid.

    Submitted 17 October, 2016; v1 submitted 5 October, 2015; originally announced October 2015.

    Comments: 27 pages

    Report number: CPH-SYM-DNRF92 MSC Class: 53D55

    Journal ref: Compositio Math. 153 (2017) 41-67

  193. Non-commutativity of the central sequence algebra for separable non-type I C$^{\ast}$-algebras

    Authors: Hiroshi Ando, Eberhard Kirchberg

    Abstract: We show that if $A$ is a separable, simple and non-type I C$^{\ast}$ algebra, then for every properly infinite hyperfinite von Neumann algebra $M$ with separable predual, its Ocneanu ultrapower $M'\cap M^ω$ arises as a sub-quotient of the central sequence algebra $F(A)$ defined by the second named author. In particular, this answers affirmatively the question of the second named author (Abel Sympo… ▽ More

    Submitted 12 May, 2016; v1 submitted 1 October, 2015; originally announced October 2015.

    Comments: 15 pages, same as the published version. We added Ozawa's proof (using Kishimoto-Ozawa-Sakai Theorem) of non-commutativity of F(A) in Appendix

    Report number: CPH-SYM-DNRF92

  194. arXiv:1510.00326  [pdf, other

    math.DS

    Flow Equivalence of Shift Spaces

    Authors: Peter Michael Reichstein Rasmussen

    Abstract: We study two problems related to flow equivalence of shift spaces. The first problem, the classification of $S$-gap shifts up to flow equivalence, is partially solved with the establishment of a new invariant for the sofic $S$-gap shifts and a complete classification of the non-sofic $S$-gap shifts. The second problem is an examination of the entropy of shift spaces under flow equivalence. For a w… ▽ More

    Submitted 29 September, 2015; originally announced October 2015.

    Comments: 42 pages, 4 figures

    Report number: CPH-SYM-DNRF92 MSC Class: 37B10

  195. arXiv:1509.09274  [pdf, ps, other

    math.AG math.AT math.QA

    Brown's dihedral moduli space and freedom of the gravity operad

    Authors: Johan Alm, Dan Petersen

    Abstract: Francis Brown introduced a partial compactification $M_{0,n}^δ$ of the moduli space $M_{0,n}$. We prove that the gravity cooperad, given by the degree-shifted cohomologies of the spaces $M_{0,n}$, is cofree as a nonsymmetric anticyclic cooperad; moreover, the cogenerators are given by the cohomology groups of $M_{0,n}^δ$. This says in particular that $H^\bullet(M_{0,n}^δ)$ injects into… ▽ More

    Submitted 30 July, 2016; v1 submitted 30 September, 2015; originally announced September 2015.

    Comments: 39 pages. v2: significant revision, to appear in the Annales Scientifiques de l'ENS

    Report number: CPH-SYM-DNRF92

    Journal ref: Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 5, 1081--1122

  196. The spectrum of the equivariant stable homotopy category of a finite group

    Authors: Paul Balmer, Beren Sanders

    Abstract: We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in determining its topology and obtain a complete answer for groups of square-free order. For general finite groups, we describe the topology up to an unresolved indetermi… ▽ More

    Submitted 2 September, 2016; v1 submitted 17 August, 2015; originally announced August 2015.

    Comments: 34 pages, to appear in Invent. Math

    Report number: CPH-SYM-DNRF92

    Journal ref: Invent. Math. 208 (2017) 283-326

  197. arXiv:1508.03433  [pdf, other

    math.AT math.GT math.QA

    Comparing fat graph models of moduli space

    Authors: Daniela Egas Santander

    Abstract: Godin introduced the categories of open closed fat graphs $Fat^{oc}$ and admissible fat graphs $Fat^{ad}$ as models of the mapping class group of open closed cobordism. We use the contractibility of the arc complex to give a new proof of Godin's result that $Fat^{ad}$ is a model of the mapping class group of open-closed cobordisms. Similarly, Costello introduced a chain complex of black and white… ▽ More

    Submitted 14 August, 2015; originally announced August 2015.

    Comments: 45 pages, 24 figures

    Report number: CPH-SYM-DNRF92 MSC Class: 32G15; 57M15; 57R56

  198. arXiv:1508.03129  [pdf, other

    math.AT math.KT

    Topological Hochschild homology and the cyclic bar construction in symmetric spectra

    Authors: Irakli Patchkoria, Steffen Sagave

    Abstract: The cyclic bar construction in symmetric spectra and Bökstedt's original construction are two possible ways to define the topological Hochschild homology of a symmetric ring spectrum. In this short note we explain how to correct an error in Shipley's original comparison of these two approaches.

    Submitted 18 November, 2015; v1 submitted 13 August, 2015; originally announced August 2015.

    Comments: v2: 7 pages; exposition improved, accepted for publication in Proceedings of the AMS

    Report number: CPH-SYM-DNRF92 MSC Class: 55P43

    Journal ref: Proc. Amer. Math. Soc. 144 (2016), no. 9, 4099-4106

  199. arXiv:1508.02426  [pdf, other

    math.CO

    A note on independence complexes of chordal graphs and dismantling

    Authors: Michal Adamaszek

    Abstract: We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs.

    Submitted 10 August, 2015; originally announced August 2015.

    Comments: 8 pages

    Report number: CPH-SYM-DNRF92

  200. arXiv:1508.00389  [pdf, ps, other

    math.OA

    Lifting theorems for completely positive maps

    Authors: James Gabe

    Abstract: We prove lifting theorems for completely positive maps going out of exact $C^\ast$-algebras, where we remain in control of which ideals are mapped into which. A consequence is, that if $\mathsf X$ is a second countable topological space, $\mathfrak A$ and $\mathfrak B$ are separable, nuclear $C^\ast$-algebras over $\mathsf X$, and the action of $\mathsf X$ on $\mathfrak A$ is continuous, then… ▽ More

    Submitted 30 January, 2022; v1 submitted 3 August, 2015; originally announced August 2015.

    Comments: 27 pages. V4: Accepted version (to appear in J. Noncommut. Geom.). V3: Major revision has been made, as a result upon which the earlier versions were based, has been found to contain an error. This has not affected the main results. Certain other parts have been significantly changed to improve readability. Also, new applications have been included

    Report number: CPH-SYM-DNRF92 MSC Class: 46L05; 46L35; 46L80