{
  "id": "0712.4060",
  "version": "v1",
  "published": "2007-12-25T11:32:14.000Z",
  "updated": "2007-12-25T11:32:14.000Z",
  "title": "A class function on the mapping class group of an orientable surface and the Meyer cocycle",
  "authors": [
    "Masatoshi Sato"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we define a $\\mathbf{QP}^1$-valued class function on the mapping class group $\\mathcal{M}_{g,2}$ of a surface $\\Sigma_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a $\\Sigma_{g,2}$ bundle over a pair of pants $P$. Gluing to $E$ the product of an annulus and $P$ along the boundaries of each fiber, we obtain a closed surface bundle over $P$. We have another closed surface bundle by gluing to $E$ the product of $P$ and two disks. The sign of our class function cobounds the 2-cocycle on $\\mathcal{M}_{g,2}$ defined by the difference of the signature of these two surface bundles over $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-25T11:32:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N13",
      "55R40"
    ],
    "keywords": [
      "mapping class group",
      "meyer cocycle",
      "orientable surface",
      "closed surface bundle",
      "class function cobounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.4060S"
    }
  }
}