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Real versus complex K–theory using Kasparov’s bivariant KK–theory
Schick, Thomas1
1Fachbereich Mathematik, Georg-August-Universität Göttingen, Germany
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 333-346
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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.

DOI : 10.2140/agt.2004.4.333
Keywords: real $K$–theory, complex $K$–theory, bivariant $K$–theory

Schick, Thomas  1

1 Fachbereich Mathematik, Georg-August-Universität Göttingen, Germany 
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Schick, Thomas. Real versus complex K–theory using Kasparov’s bivariant KK–theory. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 333-346. doi: 10.2140/agt.2004.4.333

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