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.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Annals of K-Theory |
Vol/bind | 8 |
Udgave nummer | 2 |
Sider (fra-til) | 221-243 |
Antal sider | 23 |
ISSN | 2379-1683 |
DOI | |
Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
MG was supported by the Swedish Research Council Grant VR 2018-0350. MSC2020: primary 58J22; secondary 18F25, 19D55, 26A16. Keywords: cyclic cohomology, Lipschitz algebras, singular traces, algebraic K-theory.
Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).
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