{
  "id": "1212.0983",
  "version": "v2",
  "published": "2012-12-05T10:09:18.000Z",
  "updated": "2013-02-05T11:36:10.000Z",
  "title": "II$_1$ factors and equivalence relations with distinct fundamental groups",
  "authors": [
    "Jan Keersmaekers",
    "An Speelman"
  ],
  "comment": "v2: Some minor adjustments were made. Accepted for publication in International Journal of Mathematics",
  "categories": [
    "math.OA"
  ],
  "abstract": "We construct a group measure space II$_1$ factor that has two non-conjugate Cartan subalgebras. We show that the fundamental group of the II$_1$ factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is non-trivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-05T11:36:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distinct fundamental groups",
      "equivalence relation",
      "group measure space",
      "second cartan subalgebra",
      "non-conjugate cartan subalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0983K"
    }
  }
}