Bundles of C*-algebras and the KK(X;-,-)-bifunctor

Details Bundles of C*-algebras and the KK(X;-,-)-bifunctor Bundles of C*-algebras and the KK(X;-,-)-bifunctor

2007-11-22

arxiv.org/abs/0711.3568v1

Proc. Conf. C*-algebras and elliptic theory, Trends in Mathematics (2006) 313-327

Mathematics

K-Theory and Homology

16 pages; uses xy.sty

Scientific paper

An overview about C*-algebra bundles with a Z-grading is presented, with particular emphasis on classification questions. In particular, we discuss the role of the representable KK(X ; -, -)-bifunctor introduced by Kasparov. As an application, we consider Cuntz-Pimsner algebras associated with vector bundles, and give a classification in terms of K-theoretical invariants in the case in which the base space is an n-sphere.

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