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Exotic cyclic cohomology
classes and Lipschitz algebras
Magnus Goffeng and Ryszard Nest |
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Vol. 8 (2023), No. 2, 221–243
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Abstract |
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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 -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 -theory. |
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Keywords
cyclic cohomology, Lipschitz algebras, singular traces,
algebraic $K\mkern-2mu$-theory
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Mathematical Subject Classification
Primary: 58J22
Secondary: 18F25, 19D55, 26A16
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Milestones
Received: 6 May 2022
Revised: 26 January 2023
Accepted: 15 February 2023
Published: 14 June 2023
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Authors |
| Magnus Goffeng | |
| Centre for Mathematical
Sciences University of Lund Lund Sweden |
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| Ryszard Nest | |
| Department of Mathematical
Sciences University of Copenhagen Copenhagen Denmark |
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| © 2023 MSP (Mathematical Sciences Publishers). |
