{
  "id": "math/9811082",
  "version": "v1",
  "published": "1998-11-12T10:43:04.000Z",
  "updated": "1998-11-12T10:43:04.000Z",
  "title": "Dehn surgery and negatively curved 3-manifolds",
  "authors": [
    "Daryl Cooper",
    "Marc Lackenby"
  ],
  "comment": "35 pages, 2 figures. To be published in JDG",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that, for any given 3-manifold M, there are at most finitely many hyperbolic knots K in the 3-sphere and fractions p/q (with q > 22), such that M is obtained by p/q surgery along K. This is a corollary of the following result. If M is obtained by Dehn filling the cusps of a hyperbolic 3-manifold X, where each filling slope has length more than 2 \\pi + \\epsilon, then, for any given M and \\epsilon > 0, there are only finitely many possibilities for X and for the filling slopes. In this paper, we also investigate the length of boundary slopes, and sequences of negatively curved metrics on a given 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-12T10:43:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M25"
    ],
    "keywords": [
      "dehn surgery",
      "filling slope",
      "p/q surgery",
      "hyperbolic knots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11082C"
    }
  }
}