Real versus complex K-theory using Kasparov's bivariant KK-theory

Details Real versus complex K-theory using Kasparov's bivariant KK-theory Real versus complex K-theory using Kasparov's bivariant KK-theory

2003-11-17

arxiv.org/abs/math/0311295v3

Algebr. Geom. Topol. 4 (2004) 333-346

Mathematics

K-Theory and Homology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-18.abs.html

Scientific paper

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.

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