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

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 (slightly 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.

A shorter (but less self contained) version, relying on the work of Boersema, can be found at http://www.uni-math.gwdg.de/schick/publ/real_complex_K.html

-- (Goettingen)


Thomas Schick <schick@uni-math.gwdg.de>