The $KH$-Isomorphism Conjecture and Algebraic $KK$-theory

Details The $KH$-Isomorphism Conjecture and Algebraic $KK$-theory The $KH$-Isomorphism Conjecture and Algebraic $KK$-theory

2007-11-14

arxiv.org/abs/0711.2181v2

Mathematics

K-Theory and Homology

Scientific paper

In this article we prove that the $KH$-asembly map, as defined by Bartels and
L{\"u}ck, can be described in terms of the algebraic $KK$-theory of Cortinas
and Thom. The $KK$-theory description of the $KH$-assembly map is similar to
that of the Baum-Connes assembly map. In very elementary cases, methods used to
prove the Baum-Connes conjecture also apply to the $KH$-isomorphism conjecture.

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