{
  "id": "1103.4680",
  "version": "v2",
  "published": "2011-03-24T05:00:59.000Z",
  "updated": "2011-06-16T23:52:53.000Z",
  "title": "Reduced Bers boundaries of Teichmüller spaces",
  "authors": [
    "Ken'ichi Ohshika"
  ],
  "comment": "Ver 2: minor corrections",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider a quotient space of the Bers boundary of Teichm\\\"{u}ller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point. This reduced Bers boundary turns out to be independent of the basepoint, and the action of the mapping class group on the Teichm\\\"{u}ller space extends continuously to this boundary. We show that every auto-homeomorphism on the reduced Bers boundary comes from an extended mapping class. We also give a way to determine the limit in the reduced Bers boundary up to some ambiguity for parabolic curves for a given sequence in the Teichm\\\"{u}ller space, by generalising the Thurston compactification.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-16T23:52:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "30F40",
      "30F60",
      "57M60"
    ],
    "keywords": [
      "teichmüller spaces",
      "reduced bers boundary comes",
      "quasi-conformal deformation space",
      "reduced bers boundary turns",
      "mapping class group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4680O"
    }
  }
}