{
  "id": "0905.1318",
  "version": "v1",
  "published": "2009-05-08T19:44:48.000Z",
  "updated": "2009-05-08T19:44:48.000Z",
  "title": "Jørgensen Number and Arithmeticity",
  "authors": [
    "Jason Callahan"
  ],
  "comment": "27 pages, 2 figures",
  "journal": "Conform. Geom. Dyn. 13 (2009), 160-186",
  "doi": "10.1090/S1088-4173-09-00196-9",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "A J{\\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\\o}rgensen's Inequality. This paper shows that the only torsion-free J{\\o}rgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic J{\\o}rgensen groups, and establishes a characterization of cocompact arithmetic J{\\o}rgensen groups. The paper also defines and computes the J{\\o}rgensen number of several non-cocompact Kleinian groups including some two-bridge knot and link groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-08T19:44:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40",
      "57M05",
      "57M07",
      "57M25",
      "57M50"
    ],
    "keywords": [
      "jørgensen number",
      "arithmeticity",
      "non-elementary kleinian group",
      "non-cocompact kleinian groups",
      "figure-eight knot group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Conform. Geom. Dyn."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}