{
  "id": "1711.00895",
  "version": "v1",
  "published": "2017-11-02T19:14:10.000Z",
  "updated": "2017-11-02T19:14:10.000Z",
  "title": "Intersections of multicurves from Dynnikov coordinates",
  "authors": [
    "S. Öykü Yurttas",
    "Toby Hall"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We present an algorithm for calculating the geometric intersection number of two multicurves on the $n$-punctured disk, taking as input their Dynnikov coordinates. The algorithm has complexity $O(m^2n^4)$, where $m$ is the sum of the absolute values of the Dynnikov coordinates of the two multicurves. The main ingredient is an algorithm due to Cumplido for relaxing a multicurve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-02T19:14:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57N16",
      "20F36"
    ],
    "keywords": [
      "dynnikov coordinates",
      "multicurve",
      "geometric intersection number",
      "absolute values",
      "main ingredient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}