{
  "id": "1703.04190",
  "version": "v1",
  "published": "2017-03-12T22:36:50.000Z",
  "updated": "2017-03-12T22:36:50.000Z",
  "title": "On finiteness properties of the Johnson filtrations",
  "authors": [
    "Mikhail Ershov",
    "Sue He"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let A denote either the automorphism group of the free group of rank n>=4 or the mapping class group of an orientable surface of genus n>=12 with 1 boundary component, and let G be either the subgroup of IA-automorphisms or the Torelli subgroup of A, respectively. We prove that any subgroup of G containing [G,G] (in particular, the Johnson kernel in the mapping class group case) is finitely generated. We also prove that if N<=1+n/12 and K is any subgroup of G containing the Nth term of the lower central series of G (for instance, if K is the Nth term of the Johnson filtration of G), then the abelianization K/[K,K] is finitely generated. Finally, we prove that if H is any finite index subgroup of A containing the Nth term of the lower central series of G, with N as above, then H has finite abelianization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-12T22:36:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28",
      "20F65",
      "20F40",
      "20J06"
    ],
    "keywords": [
      "johnson filtration",
      "finiteness properties",
      "nth term",
      "lower central series",
      "mapping class group case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}