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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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