The Baum-Connes Conjecture via Localisation of Categories

Details The Baum-Connes Conjecture via Localisation of Categories The Baum-Connes Conjecture via Localisation of Categories

2003-12-15

arxiv.org/abs/math/0312292v3

Topology, vol. 45 (2006), pp. 209-259

Mathematics

K-Theory and Homology

Scientific paper

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting.

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