{
  "id": "1810.05125",
  "version": "v1",
  "published": "2018-10-11T17:09:57.000Z",
  "updated": "2018-10-11T17:09:57.000Z",
  "title": "Knot Floer homology and the unknotting number",
  "authors": [
    "Akram Alishahi",
    "Eaman Eftekhary"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Given a knot K in S^3, let u^-(K) (respectively, u^+(K)) denote the minimum number of negative (respectively, positive) crossing changes among all unknotting sequences for K. We use knot Floer homology to construct the invariants l^-(K), l^+(K) and l(K), which give lower bounds on u^-(K), u^+(K) and the unknotting number u(K), respectively. The invariant l(K) only vanishes for the unknot, and is greater than or equal to the \\nu^-(K). Moreover, the difference l(K)-\\nu^-(K) can be arbitrarily large. We also present several applications towards bounding the unknotting number, the alteration number and the Gordian distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-11T17:09:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "knot floer homology",
      "unknotting number",
      "lower bounds",
      "gordian distance",
      "alteration number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}