{
  "id": "2101.05789",
  "version": "v1",
  "published": "2021-01-14T18:49:04.000Z",
  "updated": "2021-01-14T18:49:04.000Z",
  "title": "Evaluations of link polynomials and recent constructions in Heegaard Floer theory",
  "authors": [
    "Larry Gu",
    "Andrew Manion"
  ],
  "comment": "18 pages; 2 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "Using a definition of Euler characteristic for fractionally-graded complexes based on roots of unity, we show that the Euler characteristics of Dowlin's \"$\\mathfrak{sl}(n)$-like\" Heegaard Floer knot invariants $HFK_n$ recover both Alexander polynomial evaluations and $\\mathfrak{sl}(n)$ polynomial evaluations at certain roots of unity for links in $S^3$. We show that the equality of these evaluations can be viewed as the decategorified content of the conjectured spectral sequences relating $\\mathfrak{sl}(n)$ homology and $HFK_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-14T18:49:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18",
      "57K14"
    ],
    "keywords": [
      "heegaard floer theory",
      "link polynomials",
      "constructions",
      "euler characteristic",
      "heegaard floer knot invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}