{
  "id": "1910.08195",
  "version": "v1",
  "published": "2019-10-17T23:05:13.000Z",
  "updated": "2019-10-17T23:05:13.000Z",
  "title": "A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds",
  "authors": [
    "Ciprian Manolescu",
    "Marco Marengon",
    "Sucharit Sarkar",
    "Michael Willis"
  ],
  "comment": "51 pages",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We extend the definition of Khovanov-Lee homology to links in connected sums of $S^1 \\times S^2$'s, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in $S^1 \\times S^2$, we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussen-type invariant to the genus of surfaces with boundary in the following four-manifolds: $B^2 \\times S^2$, $S^1 \\times B^3$, $\\mathbb{CP}^2$, and various connected sums and boundary sums of these. We deduce that Rasmussen's invariant also gives genus bounds for surfaces inside homotopy 4-balls obtained from $B^4$ by Gluck twists. Therefore, it cannot be used to prove that such homotopy 4-balls are non-standard.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-17T23:05:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "rasmussens invariant",
      "applications",
      "four-manifolds",
      "rasmussen-type invariant",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}