{
  "id": "2312.09114",
  "version": "v1",
  "published": "2023-12-14T16:47:53.000Z",
  "updated": "2023-12-14T16:47:53.000Z",
  "title": "Local equivalence and refinements of Rasmussen's s-invariant",
  "authors": [
    "Nathan M. Dunfield",
    "Robert Lipshitz",
    "Dirk Schuetz"
  ],
  "comment": "43 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even-odd (LEO) triple. We get a homomorphism from the smooth concordance group $C$ to the resulting local equivalence group $C_{LEO}$ of such triples. We give several versions of the $s$-invariant that descend to $C_{LEO}$, including one that completely determines whether the image of a knot $K$ in $C_{LEO}$ is trivial. We discuss computer experiments illustrating the power of these invariants in obstructing sliceness, both statistically and for some interesting knots studied by Manolescu-Piccirillo. Along the way, we explore several variants of this local equivalence group, including one that is totally ordered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-14T16:47:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18",
      "57K10",
      "57-08"
    ],
    "keywords": [
      "rasmussens s-invariant",
      "refinements",
      "odd khovanov homology",
      "smooth concordance group",
      "resulting local equivalence group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}