{
  "id": "2209.00389",
  "version": "v1",
  "published": "2022-09-01T12:07:11.000Z",
  "updated": "2022-09-01T12:07:11.000Z",
  "title": "Two second Steenrod squares for odd Khovanov homology",
  "authors": [
    "Dirk Schuetz"
  ],
  "comment": "38 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Recently, Sarkar-Scaduto-Stoffregen constructed a stable homotopy type for odd Khovanov homology, hence obtaining an action of the Steenrod algebra on Khovanov homology with $\\mathbb{Z}/2\\mathbb{Z}$ coefficients. Motivated by their construction we propose a way to compute the second Steenrod square. Our construction is not unique, but we can show it to be a link invariant which gives rise to a refinement of the Rasmussen $s$-invariant with $\\mathbb{Z}/2\\mathbb{Z}$ coefficients. We expect it to be related to the second Steenrod square arising from the Sarkar-Scaduto-Stoffregen construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-01T12:07:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58K18",
      "58K10"
    ],
    "keywords": [
      "odd khovanov homology",
      "link invariant",
      "sarkar-scaduto-stoffregen construction",
      "steenrod algebra",
      "coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}