{
  "id": "0807.2030",
  "version": "v2",
  "published": "2008-07-13T12:44:43.000Z",
  "updated": "2008-11-12T14:48:05.000Z",
  "title": "Spaces of closed subgroups of locally compact groups",
  "authors": [
    "Pierre de la Harpe"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "The set $\\Cal C(G)$ of closed subgroups of a locally compact group $G$ has a natural topology which makes it a compact space. This topology has been defined in various contexts by Vietoris, Chabauty, Fell, Thurston, Gromov, Grigorchuk, and many others. The purpose of the talk was to describe the space $\\Cal C(G)$ first for a few elementary examples, then for $G$ the complex plane, in which case $\\Cal C(G)$ is a 4--sphere (a result of Hubbard and Pourezza), and finally for the 3--dimensional Heisenberg group $H$, in which case $\\Cal C(H)$ is a 6--dimensional singular space recently investigated by Martin Bridson, Victor Kleptsyn and the author \\cite{BrHK}. These are slightly expanded notes prepared for a talk given at several places: the Kortrijk workshop on {\\it Discrete Groups and Geometric Structures, with Applications III,} May 26--30, 2008; the {\\it Tripode 14,} \\'Ecole Normale Sup\\'erieure de Lyon, June 13, 2008; and seminars at the EPFL, Lausanne, and in the Universit\\'e de Rennes 1. The notes do not contain any other result than those in \\cite{BrHK}, and are not intended for publication.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-12T14:48:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D05",
      "22E25",
      "22E40"
    ],
    "keywords": [
      "locally compact group",
      "closed subgroups",
      "ecole normale superieure",
      "elementary examples",
      "natural topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2030D"
    }
  }
}