{
  "id": "2002.09709",
  "version": "v1",
  "published": "2020-02-22T14:32:05.000Z",
  "updated": "2020-02-22T14:32:05.000Z",
  "title": "Knot diagrams on a punctured sphere as a model of string figures",
  "authors": [
    "Masafumi Arai",
    "Kouki Taniyama"
  ],
  "comment": "7 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a mathematical model of string figure we consider a knot diagram on the $xy$-plane in $xyz$-space missing some straight lines parallel to the $z$-axis. These straight lines correspond to fingers. We study minimal number of crossings of these knot diagrams under Reidemeister moves missing these lines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-22T14:32:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "knot diagram",
      "string figure",
      "punctured sphere",
      "fingers prevent cancellation",
      "imaginary plane orthogonal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}