{
  "id": "1512.05422",
  "version": "v1",
  "published": "2015-12-17T00:29:30.000Z",
  "updated": "2015-12-17T00:29:30.000Z",
  "title": "Khovanov homology and knot Floer homology for pointed links",
  "authors": [
    "John A. Baldwin",
    "Adam Simon Levine",
    "Sucharit Sarkar"
  ],
  "comment": "46 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A well-known conjecture states that for any $l$-component link $L$ in $S^3$, the rank of the knot Floer homology of $L$ (over any field) is less than or equal to $2^{l-1}$ times the rank of the reduced Khovanov homology of $L$. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose $E_1$ page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field $\\mathbb{Z}_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-17T00:29:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R58"
    ],
    "keywords": [
      "knot floer homology",
      "pointed links",
      "well-known conjecture states",
      "component link",
      "reduced khovanov homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151205422B"
    }
  }
}