{
  "id": "0809.4477",
  "version": "v3",
  "published": "2008-09-25T19:30:45.000Z",
  "updated": "2011-10-28T03:31:47.000Z",
  "title": "The second rational homology group of the moduli space of curves with level structures",
  "authors": [
    "Andrew Putman"
  ],
  "comment": "27 pages, 4 figures, mild revision. To appear in Adv. Math",
  "journal": "Adv. Math. 229 (2012), 1205-1234",
  "categories": [
    "math.GT",
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let $\\Gamma$ be a finite-index subgroup of the mapping class group of a closed genus $g$ surface that contains the Torelli group. For instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary of this is that the rational Picard groups of the associated finite covers of the moduli space of curves are equal to $\\Q$. We also prove analogous results for surface with punctures and boundary components.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-28T03:31:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second rational homology group",
      "moduli space",
      "level structures",
      "spin mapping class group",
      "rational picard groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4477P"
    }
  }
}