{
  "id": "1304.7923",
  "version": "v1",
  "published": "2013-04-30T09:07:36.000Z",
  "updated": "2013-04-30T09:07:36.000Z",
  "title": "A free subgroup in the image of the 4-strand Burau representation",
  "authors": [
    "Stefan Witzel",
    "Matthew C. B. Zaremsky"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "It is known that the Burau representation of the 4-strand braid group is faithful if and only if certain matrices f and k generate a (non-abelian) free group. Regarding f and k as isometries of a euclidean building we show that f^3 and k^3 generate a free group. We give two proofs, one utilizing the metric geometry of the building, and the other using simplicial retractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-30T09:07:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "51E24",
      "57M07"
    ],
    "keywords": [
      "burau representation",
      "free subgroup",
      "free group",
      "metric geometry",
      "simplicial retractions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7923W"
    }
  }
}