{
  "id": "math/0204228",
  "version": "v3",
  "published": "2002-04-18T13:05:25.000Z",
  "updated": "2005-12-11T16:55:16.000Z",
  "title": "Dehn filling of the \"magic\" 3-manifold",
  "authors": [
    "Bruno Martelli",
    "Carlo Petronio"
  ],
  "comment": "56 pages, 10 figures, 16 tables. Some consequences of the classification added",
  "journal": "Comm. Anal. Geom. 14 (2006), 967-1024",
  "categories": [
    "math.GT"
  ],
  "abstract": "We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds, including most of those with smallest known volume. Among other consequences of this classification, we mention the following: - for every integer n we can prove that there are infinitely many hyperbolic knots in the 3-sphere having exceptional surgeries n, n+1, n+2, n+3, with n+1, n+2 giving small Seifert manifolds and n, n+3 giving toroidal manifolds; - we exhibit a 2-cusped hyperbolic manifold that contains a pair of inequivalent knots having homeomorphic complements; - we exhibit a chiral 3-manifold containing a pair of inequivalent hyperbolic knots with orientation-preservingly homeomorphic complements; - we give explicit lower bounds for the maximal distance between small Seifert fillings and any other kind of exceptional filling.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-12-11T16:55:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M20",
      "57M50"
    ],
    "keywords": [
      "non-hyperbolic dehn fillings",
      "hyperbolic manifold",
      "homeomorphic complements",
      "giving small seifert manifolds",
      "explicit lower bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4228M"
    }
  }
}