C*-algebras over topological spaces: filtrated K-theory

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Standard

C*-algebras over topological spaces : filtrated K-theory. / Meyer, Ralf; Nest, Ryszard.

In: Canadian Journal of Mathematics - Journal Canadien de Mathématiques, Vol. 64, No. 2, 2012, p. 368-408.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Meyer, R & Nest, R 2012, 'C*-algebras over topological spaces: filtrated K-theory', Canadian Journal of Mathematics - Journal Canadien de Mathématiques, vol. 64, no. 2, pp. 368-408. https://doi.org/10.4153/CJM-2011-061-x

APA

Meyer, R., & Nest, R. (2012). C*-algebras over topological spaces: filtrated K-theory. Canadian Journal of Mathematics - Journal Canadien de Mathématiques, 64(2), 368-408. https://doi.org/10.4153/CJM-2011-061-x

Vancouver

Meyer R, Nest R. C*-algebras over topological spaces: filtrated K-theory. Canadian Journal of Mathematics - Journal Canadien de Mathématiques. 2012;64(2):368-408. https://doi.org/10.4153/CJM-2011-061-x

Author

Meyer, Ralf ; Nest, Ryszard. / C*-algebras over topological spaces : filtrated K-theory. In: Canadian Journal of Mathematics - Journal Canadien de Mathématiques. 2012 ; Vol. 64, No. 2. pp. 368-408.

Bibtex

@article{3b242bc192184ddda9c9ac2593b6040f,
title = "C*-algebras over topological spaces: filtrated K-theory",
abstract = "We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.",
author = "Ralf Meyer and Ryszard Nest",
year = "2012",
doi = "10.4153/CJM-2011-061-x",
language = "English",
volume = "64",
pages = "368--408",
journal = "Canadian Journal of Mathematics - Journal Canadien de Math{\'e}matiques",
issn = "0008-414X",
publisher = "University of Toronto Press * Journals Division",
number = "2",

}

RIS

TY - JOUR

T1 - C*-algebras over topological spaces

T2 - filtrated K-theory

AU - Meyer, Ralf

AU - Nest, Ryszard

PY - 2012

Y1 - 2012

N2 - We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.

AB - We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.

U2 - 10.4153/CJM-2011-061-x

DO - 10.4153/CJM-2011-061-x

M3 - Journal article

VL - 64

SP - 368

EP - 408

JO - Canadian Journal of Mathematics - Journal Canadien de Mathématiques

JF - Canadian Journal of Mathematics - Journal Canadien de Mathématiques

SN - 0008-414X

IS - 2

ER -

ID: 45182486