{
  "id": "math/0603177",
  "version": "v1",
  "published": "2006-03-08T06:38:47.000Z",
  "updated": "2006-03-08T06:38:47.000Z",
  "title": "Dimension of the Torelli group for Out(F_n)",
  "authors": [
    "Mladen Bestvina",
    "Kai-Uwe Bux",
    "Dan Margalit"
  ],
  "comment": "27 pages, 9 figures",
  "doi": "10.1007/s00222-007-0055-0",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-08T06:38:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F28"
    ],
    "keywords": [
      "torelli group",
      "combinatorial morse theory",
      "natural map",
      "eilenberg-maclane space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2007,
      "month": "May",
      "volume": 170,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InMat.170....1B"
    }
  }
}