{
  "id": "0812.0858",
  "version": "v2",
  "published": "2008-12-04T05:30:01.000Z",
  "updated": "2009-03-13T21:10:48.000Z",
  "title": "The length of unknotting tunnels",
  "authors": [
    "Daryl Cooper",
    "Marc Lackenby",
    "Jessica S. Purcell"
  ],
  "comment": "20 pages, 6 figures. 20 pages, 6 figures. Daryl Cooper added as author. V2 contains two new sections, including a second proof of the main result, and a proof that the result holds for knots in homology spheres",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-13T21:10:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "colin adams",
      "old question",
      "arbitrarily long unknotting tunnel",
      "tunnel number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0858C"
    }
  }
}