1104.4835 (Snigdhayan Mahanta)

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

Snigdhayan Mahanta

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).

View original: http://arxiv.org/abs/1104.4835