arXiv math/03112952003-11math.KTmath.OA

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

Thomas Schick

备注：: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-18.abs.html
发表信息：: Algebr. Geom. Topol. 4 (2004) 333-346
DOI：: 10.2140/agt.2004.4.333

英文摘要：

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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