{
  "id": "1701.00880",
  "version": "v1",
  "published": "2017-01-04T01:45:32.000Z",
  "updated": "2017-01-04T01:45:32.000Z",
  "title": "On Conway mutation and link homology",
  "authors": [
    "Peter Lambert-Cole"
  ],
  "comment": "38 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a new, elementary proof that Khovanov homology with $\\mathbb{Z}/2\\mathbb{Z}$--coefficients is invariant under Conway mutation. This proof also gives a strategy to prove Baldwin and Levine's conjecture that $\\delta$--graded knot Floer homology is mutation--invariant. Using the Clifford module structure on $\\widetilde{\\text{HFK}}$ induced by basepoint maps, we carry out this strategy for mutations on a large class of tangles. Let $L'$ be a link obtained from $L$ by mutating the tangle $T$. Suppose some rational closure of $T$ corresponding to the mutation is the unlink on any number of components. Then $L$ and $L'$ have isomorphic $\\delta$--graded $\\widehat{\\text{HFK}}$-groups over $\\mathbb{Z}/2\\mathbb{Z}$ as well as isomorphic Khovanov homology over $\\mathbb{Q}$. We apply these results to establish mutation--invariance for the infinite families of Kinoshita-Terasaka and Conway knots. Finally, we give sufficient conditions for a general Khovanov-Floer theory to be mutation--invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-04T01:45:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "conway mutation",
      "link homology",
      "isomorphic khovanov homology",
      "graded knot floer homology",
      "clifford module structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}