{
  "id": "math/0301114",
  "version": "v1",
  "published": "2003-01-11T15:53:07.000Z",
  "updated": "2003-01-11T15:53:07.000Z",
  "title": "Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary",
  "authors": [
    "Roberto Frigerio",
    "Bruno Martelli",
    "Carlo Petronio"
  ],
  "comment": "28 pages, 16 figures",
  "journal": "J. Differential Geom. 64 (2003) 425-455",
  "categories": [
    "math.GT"
  ],
  "abstract": "We define for each g>=2 and k>=0 a set M_{g,k} of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus g. Manifolds in M_{g,k} have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In addition, they do not contain closed essential surfaces. The cardinality of M_{g,k} for a fixed k has growth type g^g. We completely describe the non-hyperbolic Dehn fillings of each M in M_{g,k}, showing that, on any cusp of any hyperbolic manifold obtained by partially filling M, there are precisely 6 non-hyperbolic Dehn fillings: three contain essential discs, and the other three contain essential annuli. This gives an infinite class of large hyperbolic manifolds (in the sense of Wu) with boundary-reducible and annular Dehn fillings having distance 2, and allows us to prove that the corresponding upper bound found by Wu is sharp. If M has one cusp only, the three boundary-reducible fillings are handlebodies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-11T15:53:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M20"
    ],
    "keywords": [
      "geodesic boundary",
      "cusped hyperbolic",
      "non-hyperbolic dehn fillings",
      "contain essential discs",
      "contain closed essential surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1114F"
    }
  }
}