{
  "id": "math/0408026",
  "version": "v3",
  "published": "2004-08-02T20:58:38.000Z",
  "updated": "2009-02-09T15:59:57.000Z",
  "title": "Quadrisecants give new lower bounds for the ropelength of a knot",
  "authors": [
    "Elizabeth Denne",
    "Yuanan Diao",
    "John M Sullivan"
  ],
  "comment": "v3 is the version published by Geometry & Topology on 25 February 2006",
  "journal": "Geom. Topol. 10 (2006) 1--26",
  "doi": "10.2140/gt.2006.10.1",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-09T15:59:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "49Q10",
      "53A04"
    ],
    "keywords": [
      "lower bound",
      "ropelength",
      "special quadrisecant line",
      "nontrivial knot"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8026D"
    }
  }
}