K-theory tools for local and asymptotic cyclic cohomology

Shirbisheh, Vahid

doi:10.1090/S0002-9939-04-07807-4

K-theory tools for local and asymptotic cyclic cohomology
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Proc. Amer. Math. Soc. 133 (2005), 1185-1195 Request permission

Abstract:

A generalization of the Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology, and the result is applied to improve some formulas in asymptotic and local cyclic cohomology of $C^*$-algebras. As another application, it is shown that these cyclic theories are rigid under Rieffel’s deformation quantizations.

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