{
  "id": "2410.23455",
  "version": "v1",
  "published": "2024-10-30T20:55:31.000Z",
  "updated": "2024-10-30T20:55:31.000Z",
  "title": "Functoriality of Odd and Generalized Khovanov Homology in $\\mathbb{R}^3\\times I$",
  "authors": [
    "Jacob Migdail",
    "Stephan Wehrli"
  ],
  "comment": "51 pages, many figures in black and white",
  "categories": [
    "math.GT"
  ],
  "abstract": "We extend the generalized Khovanov bracket to smooth link cobordisms in $\\mathbb{R}^3\\times I$ and prove that the resulting theory is functorial up to global invertible scalars. The generalized Khovanov bracket can be specialized to both even and odd Khovanov homology. Particularly by setting $\\pi=-1$, we obtain that odd Khovanov homology is functorial up to sign. We end by showing that odd Khovanov homology is not functorial under smooth link cobordisms in $S^3\\times I$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-30T20:55:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18"
    ],
    "keywords": [
      "generalized khovanov homology",
      "odd khovanov homology",
      "smooth link cobordisms",
      "generalized khovanov bracket",
      "functoriality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}