{
  "id": "2011.05792",
  "version": "v1",
  "published": "2020-11-11T14:10:31.000Z",
  "updated": "2020-11-11T14:10:31.000Z",
  "title": "Signature of surface bundles and bounded cohomology",
  "authors": [
    "Ursula Hamenstädt"
  ],
  "comment": "26 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Extending a result of Morita, we show that all tautological classes of the moduli space of genus g curves are bounded. As an application, we obtain that for a surface bundle $E\\to B$ over a closed surface, the Eulder characteristic $\\chi(E)$ and the signature $\\sigma(E)$ are related by $\\vert 3 \\sigma(E)\\vert \\leq \\vert \\chi(E)\\vert$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T14:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "55N10",
      "57M07"
    ],
    "keywords": [
      "surface bundle",
      "bounded cohomology",
      "moduli space",
      "eulder characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}