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K-theory tools for local and asymptotic cyclic cohomology

Author: Vahid Shirbisheh
Journal: Proc. Amer. Math. Soc. 133 (2005), 1185-1195
MSC (2000): Primary 46L80; Secondary 46L65
Published electronically: November 1, 2004
MathSciNet review: 2117221
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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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Additional Information

Vahid Shirbisheh
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7

Keywords: \emph{KK}-theory, \emph{C*}-crossed product, local and asymptotic cyclic cohomology, excision, strong Morita equivalence, Rieffel's deformation quantizations
Received by editor(s): March 26, 2002
Received by editor(s) in revised form: December 10, 2003
Published electronically: November 1, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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