{
  "id": "1106.0947",
  "version": "v2",
  "published": "2011-06-06T01:44:03.000Z",
  "updated": "2011-10-11T19:19:44.000Z",
  "title": "Representation stability for the cohomology of the moduli space M_g^n",
  "authors": [
    "Rita Jimenez Rolland"
  ],
  "comment": "30 pages",
  "categories": [
    "math.GT",
    "math.AG",
    "math.AT",
    "math.RT"
  ],
  "abstract": "Let M_g^n be the moduli space of Riemann surfaces of genus g with n labeled marked points. We prove that, for g \\geq 2, the cohomology groups {H^i(M_g^n;Q)}_{n=1}^{\\infty} form a sequence of Sn representations which is representation stable in the sense of Church-Farb [CF]. In particular this result applied to the trivial Sn representation implies rational \"puncture homological stability\" for the mapping class group Mod_g^n. We obtain representation stability for sequences {H^i(PMod^n(M);Q)}_{n=1}^{\\infty}, where PMod^n(M) is the mapping class group of many connected manifolds M of dimension d \\geq 3 with centerless fundamental group; and for sequences {H^i(BPDiff^n(M);Q)}_{n=1}^{\\infty}, where BPDiff^n(M) is the classifying space of the subgroup PDiff^n(M) of diffeomorphisms of M that fix pointwise n distinguished points in M.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-11T19:19:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "representation stability",
      "mapping class group",
      "trivial sn representation implies rational",
      "cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0947J"
    }
  }
}