{
  "id": "1708.08383",
  "version": "v1",
  "published": "2017-08-28T15:43:33.000Z",
  "updated": "2017-08-28T15:43:33.000Z",
  "title": "Isomorphisms between big mapping class groups",
  "authors": [
    "Juliette Bavard",
    "Spencer Dowdall",
    "Kasra Rafi"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these `big' mapping classes and shows that each finite-index subgroup has finite outer automorphism group. As a key ingredient, we prove that all simplicial automorphisms between curve complexes of infinite-type orientable surfaces are induced by homeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-28T15:43:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "20F65",
      "57M07"
    ],
    "keywords": [
      "big mapping class groups",
      "isomorphism",
      "finite-index subgroup",
      "finite outer automorphism group",
      "argument additionally applies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}