{
  "id": "1904.07794",
  "version": "v1",
  "published": "2019-04-16T16:26:32.000Z",
  "updated": "2019-04-16T16:26:32.000Z",
  "title": "A generalized skein relation for Khovanov homology and a categorification of the $θ$-invariant",
  "authors": [
    "Maria Chlouveraki",
    "Dimos Goundaroulis",
    "Aristides Kontogeorgis",
    "Sofia Lambropoulou"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are able to generalize the Khovanov homology in order to obtain a categorification of the $\\theta$-invariant, which is itself a generalization of the Jones polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-16T16:26:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "khovanov homology",
      "generalized skein relation",
      "jones polynomial",
      "categorification",
      "richer link invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}