{
  "id": "1405.4745",
  "version": "v2",
  "published": "2014-05-19T14:35:00.000Z",
  "updated": "2015-03-11T09:39:47.000Z",
  "title": "On full groups of non ergodic probability measure preserving equivalence relations",
  "authors": [
    "François Le Maître"
  ],
  "comment": "New version incorporating referee's comments, to appear in Ergodic Theory and Dynamical Systems",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We give a formula relating the topological rank of the full group of an aperiodic pmp equivalence relation to the cost of its ergodic components. Furthermore, we obtain examples of full groups having a dense free subgroup whose rank is equal to the topological rank of the full group, using a Baire category argument. We then study the automatic continuity property for full groups of aperiodic equivalence relations, and find a connected metric for which they have the automatic continuity property. This allows us to give an algebraic characterization of aperiodicity for pmp equivalence relations, namely the non-existence of homomorphisms from their full groups into totally disconnected separable groups. A simple proof of the extreme amenability of full groups of hyperfinite pmp equivalence relations is also given, generalizing to the non ergodic case a result of Giordano and Pestov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-19T14:35:00.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-11T09:39:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full group",
      "ergodic probability measure preserving equivalence",
      "probability measure preserving equivalence relations",
      "non ergodic probability measure preserving"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4745L"
    }
  }
}