{
  "id": "1809.09769",
  "version": "v1",
  "published": "2018-09-26T00:41:14.000Z",
  "updated": "2018-09-26T00:41:14.000Z",
  "title": "The Knight Move Conjecture is false",
  "authors": [
    "Ciprian Manolescu",
    "Marco Marengon"
  ],
  "comment": "4 pages",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "The Knight Move Conjecture claims that the Khovanov homology of any knot decomposes as direct sums of some \"knight move\" pairs and a single \"pawn move\" pair. This is true for instance whenever the Lee spectral sequence from Khovanov homology to Q^2 converges on the second page, as it does for all alternating knots and knots with unknotting number at most 2. We present a counterexample to the Knight Move Conjecture. For this knot, the Lee spectral sequence admits a nontrivial differential of bidegree (1,8).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T00:41:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "khovanov homology",
      "knight move conjecture claims",
      "lee spectral sequence admits",
      "nontrivial differential",
      "knot decomposes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}