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arXiv · 1104.4835

Twisted K-theory, K-homology and bivariant Chern-Connes type character of some infinite dimensional spaces

Snigdhayan Mahanta
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Abstract

We study the twisted K-theory and K-homology of some infinite dimensional spaces, like SU(\infty), in the bivariant setting. Using a general procedure due to Cuntz we construct a bivariant K-theory on the category of separable \sigma-C^*-algebras that generalizes both twisted K-theory and K-homology of (locally) compact spaces. We construct a bivariant Chern--Connes type character taking values in bivariant local cyclic homology. We analyse the structure of the dual Chern--Connes character from (analytic) K-homology to local cyclic cohomology under some reasonable hypotheses. We also investigate the twisted periodic cyclic homology via locally convex algebras and the local cyclic homology via C^*-algebras (in the compact case).

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Snigdhayan Mahanta. 2011-04-26. Twisted K-theory, K-homology and bivariant Chern-Connes type character of some infinite dimensional spaces. https://doi.org/10.1215/21562261-2693460

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