{
  "id": "math/9801045",
  "version": "v1",
  "published": "1998-01-10T22:16:57.000Z",
  "updated": "1998-01-10T22:16:57.000Z",
  "title": "Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle",
  "authors": [
    "William P. Thurston"
  ],
  "comment": "32 pages, 6 figures, revision of 1986 preprint",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends toward a pair of projectively measured laminations that bind the surface, there is a convergent subsequence. This preprint also analyzes the quasi-isometric geometry of quasi-Fuchsian 3-manifolds. This eprint is based on a 1986 preprint, which was refereed and accepted for publication, but which I neglected to correct and return. The referee's corrections have now been incorporated, but it is largely the same as the 1986 version (which was a significant revision of a 1981 version).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-01-10T22:16:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surface groups",
      "hyperbolic structures",
      "conformal structures tends",
      "circle admits",
      "geometric decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......1045T"
    }
  }
}