{
  "id": "1509.02738",
  "version": "v1",
  "published": "2015-09-09T11:54:38.000Z",
  "updated": "2015-09-09T11:54:38.000Z",
  "title": "Concordance maps in knot Floer homology",
  "authors": [
    "Andras Juhasz",
    "Marco Marengon"
  ],
  "comment": "36 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that a decorated knot concordance $C$ from $K$ to $K'$ induces a homomorphism $F_C$ on knot Floer homology that preserves the Alexander and Maslov gradings. Furthermore, it induces a morphism of the spectral sequences to $\\widehat{HF}(S^3) \\cong \\mathbb{Z}_2$ that agrees with $F_C$ on the $E^1$ page and is the identity on the $E^\\infty$ page. It follows that $F_C$ is non-vanishing on $\\widehat{HFK}_0(K, \\tau(K))$. We also obtain an invariant of slice disks in homology 4-balls bounding $S^3$. If $C$ is invertible, then $F_C$ is injective, hence $\\dim \\widehat{HFK}_j(K,i) \\le \\dim \\widehat{HFK}_j(K',i)$ for every $i$, $j \\in \\mathbb{Z}$. This implies an unpublished result of Ruberman that if there is an invertible concordance from the knot $K$ to $K'$, then $g(K) \\le g(K')$, where $g$ denotes the Seifert genus. Furthermore, if $g(K) = g(K')$ and $K'$ is fibred, then so is $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-09T11:54:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "knot floer homology",
      "concordance maps",
      "maslov gradings",
      "seifert genus",
      "spectral sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150902738J"
    }
  }
}