{
  "id": "0912.3282",
  "version": "v1",
  "published": "2009-12-16T23:08:10.000Z",
  "updated": "2009-12-16T23:08:10.000Z",
  "title": "The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers",
  "authors": [
    "Yuanan Diao",
    "Claus Ernst",
    "Attila Por",
    "Uta Ziegler"
  ],
  "comment": "53 pages, 28 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For a knot or link K, let L(K) be the ropelength of K and Cr(K) be the crossing number of K. In this paper, we show that there exists a constant a>0 such that L(K) is bounded above by a Cr(K) ln^5 (Cr(K)) for any knot K. This result shows that the upper bound of the ropelength of any knot is almost linear in terms of its minimum crossing number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-16T23:08:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "ropelength",
      "minimum crossing number",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3282D"
    }
  }
}