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Exotic cyclic cohomology classes and Lipschitz algebras

Goffeng, Magnus LU orcid and Nest, Ryszard (2023) In Annals of K-Theory 8(2). p.221-243
Abstract

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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
algebraic K-theory, cyclic cohomology, Lipschitz algebras, singular traces
in
Annals of K-Theory
volume
8
issue
2
pages
23 pages
publisher
Mathematical Sciences Publishers
external identifiers
  • scopus:85162920615
ISSN
2379-1683
DOI
10.2140/akt.2023.8.221
language
English
LU publication?
yes
id
27a8a8bf-6356-4a84-a155-1ff10ce90ea5
date added to LUP
2023-09-15 13:40:17
date last changed
2025-10-14 10:32:21
@article{27a8a8bf-6356-4a84-a155-1ff10ce90ea5,
  abstract     = {{<p>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.</p>}},
  author       = {{Goffeng, Magnus and Nest, Ryszard}},
  issn         = {{2379-1683}},
  keywords     = {{algebraic K-theory; cyclic cohomology; Lipschitz algebras; singular traces}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{221--243}},
  publisher    = {{Mathematical Sciences Publishers}},
  series       = {{Annals of K-Theory}},
  title        = {{Exotic cyclic cohomology classes and Lipschitz algebras}},
  url          = {{http://dx.doi.org/10.2140/akt.2023.8.221}},
  doi          = {{10.2140/akt.2023.8.221}},
  volume       = {{8}},
  year         = {{2023}},
}