{
  "id": "1704.04449",
  "version": "v1",
  "published": "2017-04-14T15:14:27.000Z",
  "updated": "2017-04-14T15:14:27.000Z",
  "title": "Central stability for the homology of congruence subgroups and the second homology of Torelli groups",
  "authors": [
    "Jeremy Miller",
    "Peter Patzt",
    "Jennifer C. H. Wilson"
  ],
  "comment": "34 pages, 3 figures. Comments welcome",
  "categories": [
    "math.AT",
    "math.GR",
    "math.GT",
    "math.RT"
  ],
  "abstract": "We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also prove a new representation stability result for the homology of certain congruence subgroups, partially improving upon the work of Putman-Sam. These results follow from a general theorem on syzygies of certain modules with finite polynomial degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-14T15:14:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "11F75",
      "18A25",
      "55U10"
    ],
    "keywords": [
      "congruence subgroups",
      "torelli groups",
      "central stability",
      "representation stability result",
      "second homology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}