{
  "id": "math/0404445",
  "version": "v2",
  "published": "2004-04-25T19:59:22.000Z",
  "updated": "2004-10-26T15:01:34.000Z",
  "title": "Commensurations of the Johnson kernel",
  "authors": [
    "Tara E Brendle",
    "Dan Margalit"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper37.abs.html",
  "journal": "Geom. Topol. 8(2004) 1361-1384",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let K be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. Assuming that S is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that Comm(K), Aut(K) and Mod(S) are all isomorphic. More generally, we show that any injection of a finite index subgroup of K into the Torelli group I of S is induced by a homeomorphism. In particular, this proves that K is co-Hopfian and is characteristic in I. Further, we recover the result of Farb and Ivanov that any injection of a finite index subgroup of I into I is induced by a homeomorphism. Our method is to reformulate these group theoretic statements in terms of maps of curve complexes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-26T15:01:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "20F38",
      "20F36"
    ],
    "keywords": [
      "johnson kernel",
      "finite index subgroup",
      "commensurations",
      "group theoretic statements",
      "extended mapping class group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4445B"
    }
  }
}