{
  "id": "0910.5190",
  "version": "v1",
  "published": "2009-10-27T17:50:50.000Z",
  "updated": "2009-10-27T17:50:50.000Z",
  "title": "Mapping class groups of medium distance Heegaard splittings",
  "authors": [
    "Jesse Johnson"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that given two handlebody sets in the curve complex for a surface that are distance at least four apart, the group of automorphisms of the curve complex that preserve both handlebody sets is finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-27T17:50:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "medium distance heegaard splittings",
      "curve complex",
      "handlebody sets",
      "hempel distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5190J"
    }
  }
}