Equivariant geometric K-homology for compact Lie group actions
arXiv:0902.0641 · doi:10.1007/s12188-010-0034-z
Abstract
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.
25 pages. v2: some mistakes corrected, more detail added, Michael Walter as author added. To appear in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg