{
  "id": "math/0509311",
  "version": "v1",
  "published": "2005-09-14T13:19:46.000Z",
  "updated": "2005-09-14T13:19:46.000Z",
  "title": "Countable groups are mapping class groups of hyperbolic 3-manifolds",
  "authors": [
    "Roberto Frigerio",
    "Bruno Martelli"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-14T13:19:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "20F29",
      "30F40"
    ],
    "keywords": [
      "mapping class group",
      "countable group",
      "hyperbolic",
      "outer automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9311F"
    }
  }
}