%0 Journal Article
%T Equivariant extension properties of coset spaces of locally compact groups and approximate slices
%A Sergey A. Antonyan
%J Mathematics
%D 2011
%I arXiv
%X We prove that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally contractible, (4) $G/H$ is an ANE for paracompact spaces, (5) $G/H$ is a metrizable $G$-ANE for paracompact proper $G$-spaces having a paracompact orbit space. A new version of the Approximate slice theorem is also proven in the light of these results.
%U http://arxiv.org/abs/1103.0804v1