{
  "id": "math/9910099",
  "version": "v2",
  "published": "1999-10-19T18:09:16.000Z",
  "updated": "2000-10-13T15:01:49.000Z",
  "title": "Levelling an unknotting tunnel",
  "authors": [
    "Hiroshi Goda",
    "Martin Scharlemann",
    "Abigail Thompson"
  ],
  "comment": "Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper8.abs.html",
  "journal": "Geom. Topol. 4(2000) 243-275",
  "categories": [
    "math.GT"
  ],
  "abstract": "It is a consequence of theorems of Gordon-Reid [Tangle decompositions of tunnel number one knots and links, J. Knot Theory and its Ramifications, 4 (1995) 389-409] and Thompson [Thin position and bridge number for knots in the 3-sphere, Topology, 36 (1997) 505-507] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [A note on unknotting tunnels for 2-bridge knots, Bulletin of Faculty of Engineering Takushoku University, 3 (1992) 219-225], who showed that the (now known) classification of unknotting tunnels for 2-bridge knots would follow quickly if it were known that any unknotting tunnel can be made level.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-10-13T15:01:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "unknotting tunnel",
      "tunnel number",
      "thin position",
      "engineering takushoku university",
      "bridge position"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}