{
  "id": "1103.0804",
  "version": "v1",
  "published": "2011-03-03T23:48:57.000Z",
  "updated": "2011-03-03T23:48:57.000Z",
  "title": "Equivariant extension properties of coset spaces of locally compact groups and approximate slices",
  "authors": [
    "Sergey A. Antonyan"
  ],
  "categories": [
    "math.GN",
    "math.GR",
    "math.GT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-03T23:48:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D05",
      "22F05",
      "54C55",
      "54H15"
    ],
    "keywords": [
      "equivariant extension properties",
      "locally compact groups",
      "coset spaces",
      "locally compact hausdorff group",
      "paracompact orbit space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0804A"
    }
  }
}