{
  "id": "math/0110174",
  "version": "v1",
  "published": "2001-10-17T08:34:59.000Z",
  "updated": "2001-10-17T08:34:59.000Z",
  "title": "Crossing number of links formed by edges of a triangulation",
  "authors": [
    "Simon A. King"
  ],
  "comment": "4 pages",
  "journal": "J. Knot Theory Ramifications 12 (2003) 281-286",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the crossing number of links that are formed by edges of a triangulation T of the 3-sphere with n tetrahedra. We show that the crossing number is bounded from above by an exponential function of n^2. In general, this bound can not be replaced by a subexponential bound. However, if T is polytopal (resp. shellable) then there is a quadratic (resp. biquadratic) upper bound in n for the crossing number. In our proof, we use a numerical invariant p(T), called polytopality, that we have introduced in math.GT/0009216.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-17T08:34:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57Q15",
      "52C45",
      "52B22"
    ],
    "keywords": [
      "crossing number",
      "triangulation",
      "exponential function",
      "subexponential bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10174K"
    }
  }
}