{
  "id": "1608.02608",
  "version": "v1",
  "published": "2016-08-08T20:15:00.000Z",
  "updated": "2016-08-08T20:15:00.000Z",
  "title": "Quadrisecants and essential secants of knots: with applications to the geometry of knots",
  "authors": [
    "Elizabeth Denne"
  ],
  "comment": "17 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A quadrisecant line is one which intersects a curve in at least four points, while an essential secant captures something about the knottedness of a knot. This survey article gives a brief history of these ideas, and shows how they may be applied to questions about the geometry of a knot via the total curvature, ropelength and distortion of a knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-08T20:15:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "applications",
      "essential secant captures",
      "quadrisecant line",
      "survey article",
      "brief history"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}