{
  "id": "math/0210245",
  "version": "v2",
  "published": "2002-10-16T15:44:38.000Z",
  "updated": "2002-10-16T21:48:55.000Z",
  "title": "Upper Bounds for Ropelength as a Function of Crossing Number",
  "authors": [
    "Jason Cantarella",
    "X. W. Faber",
    "Chad A. Mullikin"
  ],
  "comment": "11 pages, 14 figures. Replacement corrects EPS font problem in figure",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "The paper provides bounds for the ropelength of a link in terms of the crossing numbers of its split components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial improvement on previous results. The proof depends essentially on writing links in terms of their arc-presentations, and has as a key ingredient Bae and Park's theorem that an n-crossing link has an arc-presentation with less than or equal to n+2 arcs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-10-16T21:48:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10"
    ],
    "keywords": [
      "crossing number",
      "upper bounds",
      "ropelength",
      "split components",
      "earlier papers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10245C"
    }
  }
}