{
  "id": "1501.05293",
  "version": "v1",
  "published": "2015-01-21T20:53:23.000Z",
  "updated": "2015-01-21T20:53:23.000Z",
  "title": "On a triply graded Khovanov homology",
  "authors": [
    "Krzysztof K. Putyra"
  ],
  "comment": "21 pages. Some diagrams use colors, but they are readable when printed black and white",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Cobordisms are naturally bigraded and we show that this grading extends to Khovanov homology, making it a triply graded theory. Although the new grading does not make the homology a stronger invariant, it can be used to show that odd Khovanov homology is multiplicative with respect to disjoint unions and connected sums of links; same results hold for the generalized Khovanov homology defined by the author in his previous work. We also examine the module structure on both odd and even Khovanov homology, in particular computing the effect of sliding a basepoint through a crossing on the integral homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-21T20:53:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N35",
      "57M27"
    ],
    "keywords": [
      "triply graded khovanov homology",
      "odd khovanov homology",
      "generalized khovanov homology",
      "results hold",
      "disjoint unions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105293P"
    }
  }
}