{
  "id": "1611.09415",
  "version": "v1",
  "published": "2016-11-28T22:39:03.000Z",
  "updated": "2016-11-28T22:39:03.000Z",
  "title": "$τ$-invariants for knots in rational homology spheres",
  "authors": [
    "Katherine Raoux"
  ],
  "comment": "26 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Ozsv\\'ath and Szab\\'o used the knot filtration on $\\hat{CF}(S^3)$ to define the $\\tau$-invariant for knots in $S^3$. In this article we generalize their construction and define a collection of invariants $\\{\\tau_\\mathfrak{s}(Y,K)\\}_{\\mathfrak{s}\\in\\S(Y)}$ for rationally null-homologous knots in rational homology spheres. We also show that these invariants can be used to obtain a lower bound on the genus of a surface with boundary $K$ properly embedded in a negative definite 4-manifold with boundary $Y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T22:39:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational homology spheres",
      "lower bound",
      "knot filtration",
      "construction",
      "collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}