{
  "id": "1203.6551",
  "version": "v1",
  "published": "2012-03-29T15:06:17.000Z",
  "updated": "2012-03-29T15:06:17.000Z",
  "title": "On the number of hyperbolic 3-manifolds of a given volume",
  "authors": [
    "Craig Hodgson",
    "Hidetoshi Masai"
  ],
  "comment": "25 pages, 15 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "The work of Jorgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. We show that there is an infinite sequence of closed orientable hyperbolic 3-manifolds, obtained by Dehn filling on the figure eight knot complement, that are uniquely determined by their volumes. This gives a sequence of distinct volumes x_i converging to the volume of the figure eight knot complement with N(x_i) = 1 for each i. We also give an infinite sequence of 1-cusped hyperbolic 3-manifolds, obtained by Dehn filling one cusp of the (-2,3,8)-pretzel link complement, that are uniquely determined by their volumes amongst orientable cusped hyperbolic 3-manifolds. Finally, we describe examples showing that the number of hyperbolic link complements with a given volume v can grow at least exponentially fast with v.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-29T15:06:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M27",
      "57N10",
      "11E16"
    ],
    "keywords": [
      "infinite sequence",
      "knot complement",
      "hyperbolic link complements",
      "distinct volumes",
      "dehn filling"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6551H"
    }
  }
}