{
  "id": "math/0603206",
  "version": "v1",
  "published": "2006-03-09T02:47:57.000Z",
  "updated": "2006-03-09T02:47:57.000Z",
  "title": "Boundary slopes of 2-bridge links determine the crossing number",
  "authors": [
    "Jim E. Hoste",
    "Patrick D. Shanahan"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found by Hatcher and Thurston. Using this formula we show that the diameter of a 2-bridge link, that is, the difference between the smallest and largest finite slopes of diagonal surfaces, is equal to the crossing number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-09T02:47:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "boundary slope",
      "crossing number",
      "links determine",
      "diagonal surface",
      "largest finite slopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3206H"
    }
  }
}