{
  "id": "2004.07056",
  "version": "v1",
  "published": "2020-04-15T12:33:14.000Z",
  "updated": "2020-04-15T12:33:14.000Z",
  "title": "The bridge number of surface links and kei colorings",
  "authors": [
    "Kouki Sato",
    "Kokoro Tanaka"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Meier and Zupan introduced bridge trisections of surface links in $S^4$ as a 4-dimensional analogue to bridge decompositions of classical links, which gives a numerical invariant of surface links called the bridge number. We prove that there exist infinitely many surface knots with bridge number $n$ for any integer $n \\geq 4$. To prove it, we use colorings of surface links by keis and give lower bounds for the bridge number of surface links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-15T12:33:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K45",
      "57K12"
    ],
    "keywords": [
      "surface links",
      "bridge number",
      "kei colorings",
      "bridge trisections",
      "bridge decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}