{
  "id": "1710.08929",
  "version": "v1",
  "published": "2017-10-24T18:00:52.000Z",
  "updated": "2017-10-24T18:00:52.000Z",
  "title": "Normal subgroups of mapping class groups and the metaconjecture of Ivanov",
  "authors": [
    "Tara Brendle",
    "Dan Margalit"
  ],
  "comment": "65 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider a large class of normal subgroups of the mapping class group of a closed surface, and we show that all members of this class have automorphism group and abstract commensurator group isomorphic to the mapping class group. A normal subgroup lies in this class if, for example, it contains a pure element whose support is contained non-peripherally in a subsurface with one boundary component and genus less than one third that of the whole surface. The proof relies on another theorem, which states that many simplicial complexes associated to a closed surface have automorphism group isomorphic to the mapping class group. These results resolve in part the metaconjecture of N.V. Ivanov, which asserts that any \"sufficiently rich\" object associated to a surface has automorphism group isomorphic to the extended mapping class group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-24T18:00:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07"
    ],
    "keywords": [
      "mapping class group",
      "automorphism group isomorphic",
      "metaconjecture",
      "abstract commensurator group isomorphic",
      "closed surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}