{
  "id": "2206.04196",
  "version": "v1",
  "published": "2022-06-08T23:48:32.000Z",
  "updated": "2022-06-08T23:48:32.000Z",
  "title": "Unknotting number and cabling",
  "authors": [
    "Jennifer Hom",
    "Tye Lidman",
    "JungHwan Park"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unknotting number of cable knots and iterated cable knots purely in terms of the winding number of the pattern. The proof uses Alishahi-Eftekhary's bounds on unknotting number from knot Floer homology together with Hanselman-Watson's computation of the knot Floer homology of cables in terms of immersed curves in the punctured torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-08T23:48:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K18"
    ],
    "keywords": [
      "unknotting number",
      "knot floer homology",
      "hanselman-watsons computation",
      "lower bound",
      "alishahi-eftekharys bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}