{
  "id": "0912.2697",
  "version": "v2",
  "published": "2009-12-14T17:52:30.000Z",
  "updated": "2012-08-22T20:19:56.000Z",
  "title": "The Dehn function of SL(n;Z)",
  "authors": [
    "Robert Young"
  ],
  "comment": "49 pages, 9 figures, revised version, to appear in Annals of Mathematics",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by \"shortcuts,\" we obtain words of a particular form, and we use combinatorial techniques to fill these loops.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-22T20:19:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "22E40"
    ],
    "keywords": [
      "dehn function",
      "replacing large elementary matrices",
      "combinatorial techniques",
      "varying sizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2697Y"
    }
  }
}