{
  "id": "2003.02832",
  "version": "v1",
  "published": "2020-03-05T18:58:26.000Z",
  "updated": "2020-03-05T18:58:26.000Z",
  "title": "Handle decompositions of ribbon disks and their complements",
  "authors": [
    "Jennifer Hom",
    "Sungkyung Kang",
    "JungHwan Park"
  ],
  "comment": "11 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of 2-handles in a handle decomposition of a ribbon disk complement. The strong homotopy fusion number is a lower bound for the fusion number. We give examples of ribbon knots with strong homotopy fusion number one and arbitrarily large fusion number by showing that (p,1)-cable of any ribbon knot with fusion number one has strong homotopy fusion number one and fusion number p. Our main tools are Juh\\'asz-Miller-Zemke's bound on fusion number coming from the torsion order of knot Floer homology and Hanselman-Watson's cabling formula for immersed curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-05T18:58:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K40",
      "57K18",
      "57N70"
    ],
    "keywords": [
      "strong homotopy fusion number",
      "handle decomposition",
      "ribbon knot",
      "minimal number",
      "knot floer homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}