Exotic cyclic cohomology classes and Lipschitz algebras
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/27a8a8bf-6356-4a84-a155-1ff10ce90ea5
- author
- Goffeng, Magnus LU and Nest, Ryszard
- organization
- publishing date
- 2023-06
- 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
- 2023-09-15 13:40:17
@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}}, }