Equivariant geometric K-homology for compact Lie group actions

Details Equivariant geometric K-homology for compact Lie group actions Equivariant geometric K-homology for compact Lie group actions

2009-02-03

arxiv.org/abs/0902.0641v2

Mathematics

K-Theory and Homology

25 pages. v2: some mistakes corrected, more detail added, Michael Walter as author added. To appear in Abhandlungen aus dem Ma

Scientific paper

10.1007/s12188-010-0034-z

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant
geometric K-homology groups K^G_*(X), using an obvious equivariant version of
the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural
transformations to and from equivariant K-homology defined via KK-theory (the
"official" equivariant K-homology groups) and show that these are isomorphism.

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