Equivariant extension properties of coset spaces of locally compact groups and approximate slices

2011/03/03 by Sergey A. Antonyan, Antonyan, Sergey A.
Mathematics · #22D05 #22F05 #54C55 #54H15 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GN #math.GR #math.GT #msc:22D05 #msc:22F05 #msc:54C55 #msc:54H15

paper · pdf · doi:10.48550/arxiv.1103.0804

arxiv created 2011/03/03 · openalex publication_date 2011/03/03 · arxiv updated 2011/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Characterizing slices for proper actions of locally compact groups
• Decomposition of locally compact coset spaces
• Characterizing maximal compact subgroups
• Fibrations and coset spaces for locally compact groups
• Decompositions of locally compact contraction groups, series and extensions