{
  "id": "math/9807001",
  "version": "v3",
  "published": "1998-07-01T17:52:16.000Z",
  "updated": "1999-03-01T00:00:00.000Z",
  "title": "The classification of punctured-torus groups",
  "authors": [
    "Yair N. Minsky"
  ],
  "comment": "67 pages, published version",
  "journal": "Ann. of Math. (2) 149 (1999), no. 2, 559-626",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "Thurston's ending lamination conjecture proposes that a finitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be thought of as representations of the fundamental group of a punctured torus. As a consequence we verify the conjectural topological description of the deformation space of punctured-torus groups (including Bers' conjecture that the quasi-Fuchsian groups are dense in this space) and prove a rigidity theorem: two punctured-torus groups are quasi-conformally conjugate if and only if they are topologically conjugate.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-03-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40",
      "57M50"
    ],
    "keywords": [
      "punctured-torus groups",
      "free two-generator kleinian groups",
      "classification",
      "thurstons ending lamination conjecture",
      "finitely generated kleinian group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......7001M"
    }
  }
}