Kyoto Journal of Mathematics

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(), in the bivariant setting. Using a general procedure due to Cuntz we construct a bivariant K-theory on the category of separable σ-C-algebras that generalizes both the twisted K-theory and K-homology of (locally) compact spaces. We construct a bivariant Chern–Connes-type character taking values in a bivariant local cyclic homology. We analyze 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).

Article information

Source
Kyoto J. Math. Volume 54, Number 3 (2014), 597-640.

Dates
First available in Project Euclid: 14 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1408020880

Digital Object Identifier
doi:10.1215/21562261-2693460

Mathematical Reviews number (MathSciNet)
MR3263554

Zentralblatt MATH identifier
1309.19006

Subjects
Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60] 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 46L85: Noncommutative topology [See also 58B32, 58B34, 58J22] 46L87: Noncommutative differential geometry [See also 58B32, 58B34, 58J22]

Citation

Mahanta, Snigdhayan. Twisted ${K}$ -theory, ${K}$ -homology, and bivariant Chern–Connes type character of some infinite dimensional spaces. Kyoto J. Math. 54 (2014), no. 3, 597--640. doi:10.1215/21562261-2693460. https://projecteuclid.org/euclid.kjm/1408020880


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