{
  "id": "math/0302098",
  "version": "v2",
  "published": "2003-02-10T04:26:06.000Z",
  "updated": "2004-05-11T02:54:22.000Z",
  "title": "Non-left-orderable 3-manifold groups",
  "authors": [
    "Mieczyslaw K. Dabkowski",
    "Jozef H. Przytycki",
    "Amir A. Togha"
  ],
  "comment": "To appear in Canadian Mathematical Bull.; 12 pages, 5 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers of S^3 branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of S^3 branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the 5_2 knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-05-11T02:54:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M12",
      "20F60"
    ],
    "keywords": [
      "simple nontrivial examples",
      "hyperbolic",
      "cyclic branched covers",
      "smallest volume",
      "fibonacci groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2098D"
    }
  }
}