The equivariant homotopy type of $G$-${\rm ANR}$'s for proper actions of locally compact groups
Volume 85 / 2009
Banach Center Publications 85 (2009), 155-178
MSC: Primary 55P91; Secondary 54C55
DOI: 10.4064/bc85-0-11
Abstract
We prove that if $G$ is a locally compact Hausdorff group then every proper $G$-ANR space has the $G$-homotopy type of a $G$-CW complex. This is applied to extend the James-Segal $G$-homotopy equivalence theorem to the case of arbitrary locally compact proper group actions.
