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