Mathematics – K-Theory and Homology
Scientific paper
2011-04-26
Mathematics
K-Theory and Homology
32 pages, acknowledgements added and some minor changes made (including the title)
Scientific paper
We study the twisted K-theory and K-homology of some infinite dimensional spaces, like SU(\infty), in the framework of operator K-theory. We use bivariant K-theory for locally convex algebras, specialized to K-theory, to study the twisted K-theory of such spaces. We also investigate the twisted periodic cyclic homology via locally convex algebras and the local cyclic homology via C*-algebras (in the compact case). There is a general procedure to construct bivariant K-theories, which is due to Cuntz. We apply his formalism to the category of separable sigma-C*-algebras and construct a bivariant Chern-Connes type character taking values in Puschnigg's bivariant local cyclic homology. Finally we focus on the dual Chern-Connes character from (analytic) K-homology to local cyclic cohomology and analyse its structure under some reasonable hypotheses.
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