Compact group actions on equivariant absolute neighborhood retracts and their orbit spaces

Abstract

We apply equivariant joins to give a new and more transparent proof of the following result: if G is a compact Hausdorff group and X a G- ANR (respectively, a G- AR), then for every closed normal subgroup H of G, the H-orbit space X / H is a G / H - ANR (respectively, a G / H - AR). In particular, X / G is an ANR (respectively, an AR).