{
  "id": "1703.07732",
  "version": "v1",
  "published": "2017-03-22T16:26:27.000Z",
  "updated": "2017-03-22T16:26:27.000Z",
  "title": "The realization problem for Jørgensen numbers",
  "authors": [
    "Yasushi Yamashita",
    "Ryosuke Yamazaki"
  ],
  "comment": "13 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let G be a two generator subgroup of PSL(2,C). The Jorgensen number J(G) of G is defined by J(G)=inf{ |tr^2 A-4|+|tr[A,B]-2| ; G=<A,B>}. If G is a non-elementary Kleinian group, then J(G) >= 1. This inequality is called Jorgensen's inequality. In this paper, we show that, for any r >= 1, there exists a non-elementary Kleinian group whose Jorgensen number is equal to r. This answers a question posed by Oichi and Sato. We also present our computer generated picture which estimates Jorgensen numbers from above in the diagonal slice of Schottky space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T16:26:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40"
    ],
    "keywords": [
      "realization problem",
      "jørgensen numbers",
      "non-elementary kleinian group",
      "estimates jorgensen numbers",
      "jorgensens inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}