Exotic cyclic cohomology classes and Lipschitz algebras
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We study the noncommutative geometry of algebras of Lipschitz continuous and Hölder continuous functions, where nonclassical and novel differential geometric invariants arise. Indeed, we introduce a new class of Hochschild and cyclic cohomology classes that pair nontrivially with higher algebraic K-theory yet vanish when restricted to the algebra of smooth functions. Said cohomology classes provide additional methods to extract numerical invariants from Connes– Karoubi’s relative sequence in K-theory.
Original language | English |
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Journal | Annals of K-Theory |
Volume | 8 |
Issue number | 2 |
Pages (from-to) | 221-243 |
Number of pages | 23 |
ISSN | 2379-1683 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).
- algebraic K-theory, cyclic cohomology, Lipschitz algebras, singular traces
Research areas
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