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Exotic cyclic cohomology classes and Lipschitz algebras

Magnus Goffeng and Ryszard Nest

Vol. 8 (2023), No. 2, 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.

Keywords
cyclic cohomology, Lipschitz algebras, singular traces, algebraic $K\mkern-2mu$-theory
Mathematical Subject Classification
Primary: 58J22
Secondary: 18F25, 19D55, 26A16
Milestones
Received: 6 May 2022
Revised: 26 January 2023
Accepted: 15 February 2023
Published: 14 June 2023
Authors
Magnus Goffeng
Centre for Mathematical Sciences
University of Lund
Lund
Sweden
Ryszard Nest
Department of Mathematical Sciences
University of Copenhagen
Copenhagen
Denmark