Equivariant geometric K-homology for compact Lie group actions
K-Theory and Homology
2012-10-12 v2 Geometric Topology
Operator Algebras
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.
Keywords
Cite
@article{arxiv.0902.0641,
title = {Equivariant geometric K-homology for compact Lie group actions},
author = {Paul Baum and Herve Oyono-Oyono and Thomas Schick and Michael Walter},
journal= {arXiv preprint arXiv:0902.0641},
year = {2012}
}
Comments
25 pages. v2: some mistakes corrected, more detail added, Michael Walter as author added. To appear in Abhandlungen aus dem Mathematischen Seminar der Universit\"at Hamburg