{
  "id": "1312.6027",
  "version": "v2",
  "published": "2013-12-20T16:41:21.000Z",
  "updated": "2014-12-06T13:29:49.000Z",
  "title": "Universal properties of group actions on locally compact spaces",
  "authors": [
    "Hiroki Matui",
    "Mikael Rordam"
  ],
  "comment": "42 pages",
  "categories": [
    "math.GR",
    "math.OA"
  ],
  "abstract": "We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \\beta-compactification of G (which is a G-space in a natural way), and their minimal closed invariant subspaces. These are locally compact free G-spaces, and the latter are also minimal. We examine the properies of these G-spaces with emphasis on their universal properties. As an example of our resuts, we use combinatorial methods to show that each countable infinite group admits a free minimal action on the locally compact non-compact Cantor set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-20T16:41:21.000Z",
      "abstract": "We study universal properties of locally compact G-spaces, where G is a countable infinite group. In particular, we consider open invariant subsets of the \\beta-compactification of G (which is a G-space in a natural way), and we show that these have a universal property among locally compact G-spaces of a given type (to be defined). We prove universality and uniqueness results for the closed invariant subsets of the above mentioned open invariant subsets of the \\beta-compactification of G. We use combinatorial methods to show that each countable infinite group admits a free minimal action on the locally compact non-compact Cantor set.",
      "comment": "43 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-06T13:29:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A07",
      "46L55",
      "22F05"
    ],
    "keywords": [
      "universal properties",
      "locally compact spaces",
      "group actions",
      "countable infinite group",
      "locally compact non-compact cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6027M"
    }
  }
}