{
  "id": "0809.2034",
  "version": "v3",
  "published": "2008-09-11T19:12:04.000Z",
  "updated": "2009-02-25T15:42:35.000Z",
  "title": "The automorphism group of the free group of rank two is a CAT(0) group",
  "authors": [
    "Adam Piggott",
    "Kim Ruane",
    "Genevieve S. Walsh"
  ],
  "comment": "7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misattribution of the result \"Aut F_2 is biautomatic\" has been corrected",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-25T15:42:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "automorphism group",
      "free group",
      "braid group",
      "strands acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2034P"
    }
  }
}