{
  "id": "0711.0990",
  "version": "v2",
  "published": "2007-11-07T01:31:40.000Z",
  "updated": "2008-12-12T07:07:27.000Z",
  "title": "A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \\mathcal{M}_{g,*}",
  "authors": [
    "Yusuke Kuno"
  ],
  "comment": "10 pages; corrected typos",
  "journal": "Mathematical Proceedings of the Cambridge Philosophical Society, 146, issue 01, pp. 109-118, 2009",
  "doi": "10.1017/S0305004108001680",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "We present a formula expressing Earle's twisted 1-cocycle on the mapping class group of a closed oriented surface of genus >=2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita's twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class group, which is topologically a hyperelliptic involution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-12T07:07:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05",
      "32G15"
    ],
    "keywords": [
      "mapping class group",
      "combinatorial formula",
      "first homology group",
      "formula expressing earles"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.0990K"
    }
  }
}