{
  "id": "1402.5028",
  "version": "v1",
  "published": "2014-02-20T15:21:11.000Z",
  "updated": "2014-02-20T15:21:11.000Z",
  "title": "Uniformly recurrent subgroups",
  "authors": [
    "Eli Glasner",
    "Benjamin Weiss"
  ],
  "comment": "To appear in the AMS Proceedings of the Conference on Recent Trends in Ergodic Theory and Dynamical Systems",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in a work of M. Abert, Y. Glasner and B. Virag. Our main results are as follows. (i) It was shown by B. Weiss that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS's, that for the lamplighter group there is an ergodic measure preserving action which does not admit a minimal model. (ii) For an arbitrary countable group G, every URS can be realized as the stability system of some topologically transitive G-system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-20T15:21:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37A15",
      "20E05",
      "20E15",
      "57S20"
    ],
    "keywords": [
      "uniformly recurrent subgroup",
      "minimal model",
      "ergodic probability measure preserving g-system",
      "probability measure preserving g-system admits",
      "free ergodic probability measure preserving"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5028G"
    }
  }
}