Exotic cyclic cohomology classes and Lipschitz algebras

Abstract

We study the noncommutative geometry of algebras of Lipschitz continuous and Hölder 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.

18 pages

References in corpus (2)

• Nonclassical spectral asymptotics and Dixmier traces: From circles to contact manifolds
• Operator *-correspondences in analysis and geometry