Real versus complex K-theory using Kasparov's bivariant KK-theory
K-Theory and Homology
2014-10-01 v3 Operator Algebras
Abstract
In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the real one is, thus reproving a result of Baum and Karoubi. After inverting 2, the same is true for the injectivity or surjectivity part alone.
Cite
@article{arxiv.math/0311295,
title = {Real versus complex K-theory using Kasparov's bivariant KK-theory},
author = {Thomas Schick},
journal= {arXiv preprint arXiv:math/0311295},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-18.abs.html