{
  "id": "1101.1392",
  "version": "v2",
  "published": "2011-01-07T09:47:23.000Z",
  "updated": "2012-06-11T13:44:41.000Z",
  "title": "The abelianization of the Johnson kernel",
  "authors": [
    "Alexandru Dimca",
    "Richard Hain",
    "Stefan Papadima"
  ],
  "comment": "19 pages, second version, to appear in JEMS",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that the first complex homology of the Johnson subgroup of the Torelli group $T_g$ is a non-trivial unipotent $T_g$-module for all $g\\ge 4$ and give an explicit presentation of it as a $\\Sym H_1(T_g,\\C)$-module when $g\\ge 6$. We do this by proving that, for a finitely generated group $G$ satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel $K$ is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of $G$. In this setup, we also obtain a precise nilpotence test.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-11T13:44:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F34",
      "57N05",
      "16W80",
      "20F40",
      "55N25"
    ],
    "keywords": [
      "johnson kernel",
      "abelianization",
      "precise nilpotence test",
      "infinitesimal alexander invariant",
      "first complex homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1392D"
    }
  }
}