{
  "id": "math/0307039",
  "version": "v3",
  "published": "2003-07-02T22:39:27.000Z",
  "updated": "2004-02-19T15:46:26.000Z",
  "title": "Every mapping class group is generated by 6 involutions",
  "authors": [
    "Tara E. Brendle",
    "Benson Farb"
  ],
  "comment": "15 pages, 7 figures; slightly improved main result; minor revisions. to appear in J. Alg",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate Mod_{g,b}. We answer Luo's question by proving that 3 torsion elements suffice to generate Mod_{g,0}. We also prove the more delicate result that there is an upper bound, independent of genus, not only for the number of torsion elements needed to generate Mod_{g,b} but also for the order of those elements. In particular, our main result is that 6 involutions (i.e. orientation-preserving diffeomorphisms of order two) suffice to generate Mod_{g,b} for every genus g >= 3, b = 0, and g >= 4, b = 1.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-02-19T15:46:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07",
      "20F38"
    ],
    "keywords": [
      "mapping class group",
      "involutions",
      "universal upper bound",
      "torsion elements suffice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7039B"
    }
  }
}