{
  "id": "1408.6242",
  "version": "v1",
  "published": "2014-08-26T20:08:22.000Z",
  "updated": "2014-08-26T20:08:22.000Z",
  "title": "On the second homology group of the Torelli subgroup of Aut(F_n)",
  "authors": [
    "Matthew B. Day",
    "Andrew Putman"
  ],
  "comment": "39 pages",
  "categories": [
    "math.GT",
    "math.AT",
    "math.GR"
  ],
  "abstract": "Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology group of the level l congruence subgroup of Aut(F_n). Our generating set is derived from a new group presentation for IA_n which is infinite but which has a simple recursive form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-26T20:08:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second homology group",
      "torelli subgroup",
      "second rational homology group",
      "explicit finite set",
      "simple recursive form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6242D"
    }
  }
}