{
  "id": "1810.01526",
  "version": "v1",
  "published": "2018-10-02T21:26:19.000Z",
  "updated": "2018-10-02T21:26:19.000Z",
  "title": "Rank Inequalities on Knot Floer Homology of Periodic Knots",
  "authors": [
    "Keegan Boyle"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\widetilde{K}$ be a 2-periodic knot in $S^3$ with quotient $K$. We prove a rank inequality between the knot Floer homology of $\\widetilde{K}$ and the knot Floer homology of $K$ using a spectral sequence of Hendricks, Lipshitz and Sarkar. We also conjecture a filtered refinement of this inequality, for which we give computational evidence, and produce applications to the Alexander polynomials of $\\widetilde{K}$ and $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-02T21:26:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R58"
    ],
    "keywords": [
      "knot floer homology",
      "rank inequality",
      "periodic knots",
      "spectral sequence",
      "computational evidence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}