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arXiv · 2204.00361

Exotic cyclic cohomology classes and Lipschitz algebras

Magnus Goffeng·Ryszard Nest
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Abstract

We study the noncommutative geometry of algebras of Lipschitz continuous and H\"older continuous functions where non-classical and novel differential geometric invariants arise. Indeed, we introduce a new class of Hochschild and cyclic cohomology classes that pair non-trivially 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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Magnus Goffeng, Ryszard Nest. 2022-04-01. Exotic cyclic cohomology classes and Lipschitz algebras. https://doi.org/10.2140/akt.2023.8.221

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