{
  "id": "2102.12067",
  "version": "v1",
  "published": "2021-02-24T04:51:16.000Z",
  "updated": "2021-02-24T04:51:16.000Z",
  "title": "The intersection polynomials of a virtual knot",
  "authors": [
    "Ryuji Higa",
    "Takuji Nakamura",
    "Yasutaka Nakanishi",
    "Shin Satoh"
  ],
  "comment": "54 pages, 32 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study properties of the intersection polynomials and their applications concerning the behavior on symmetry, the crossing number and the virtual crossing number, a connected sum of virtual knots, characterizations of intersection polynomials, finite type invariants of order two, and a flat virtual knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T04:51:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "finite type invariants",
      "flat virtual knot",
      "third intersection polynomials",
      "intersection number",
      "study properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}