{
  "id": "1611.10330",
  "version": "v1",
  "published": "2016-11-30T19:44:22.000Z",
  "updated": "2016-11-30T19:44:22.000Z",
  "title": "Linking Numbers in Three-Manifolds",
  "authors": [
    "Patricia Cahn",
    "Alexandra Kjuchukova"
  ],
  "comment": "30 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give an explicit algorithm for computing linking numbers between curves in an irregular dihedral $p$-fold branched cover of $S^3$. This work extends a combinatorial algorithm by Perko which computes the linking number between the branch curves in the case $p=3$. Owing to the fact that every closed oriented three-manifold is a dihedral three-fold branched cover of $S^3$, the algorithm given here can be used to compute linking numbers in any three-manifold, provided that the manifold is presented as a dihedral cover of the sphere. The algorithm has been implemented in Python, and we include the code in an Appendix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-30T19:44:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25",
      "57M12"
    ],
    "keywords": [
      "three-manifold",
      "dihedral three-fold branched cover",
      "work extends",
      "combinatorial algorithm",
      "irregular dihedral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}