{
  "id": "math/0703529",
  "version": "v2",
  "published": "2007-03-19T05:01:11.000Z",
  "updated": "2008-12-02T18:58:12.000Z",
  "title": "An infinite presentation of the Torelli group",
  "authors": [
    "Andrew Putman"
  ],
  "comment": "52 pages, 14 figures, 1 table, very heavily revised and expanded, section on obtaining presentations from group actions spun off as separate paper; to appear in GAFA",
  "journal": "Geom. Funct. Anal. 19 (2009), no. 2, 591-643.",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all \"separating twists\", all \"bounding pair maps\", and all \"commutators of simply intersecting pairs\" and whose relations all come from a short list of topological configurations of these generators on the surface. Aside from a few obvious ones, all of these relations come from a set of embeddings of groups derived from surface groups into the Torelli group. In the process of analyzing these embeddings, we derive a novel presentation for the fundamental group of a closed surface whose generating set is the set of all simple closed curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-02T18:58:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05"
    ],
    "keywords": [
      "torelli group",
      "infinite presentation",
      "simple closed curves",
      "generators consist",
      "torelli subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3529P"
    }
  }
}