{
  "id": "2205.11670",
  "version": "v1",
  "published": "2022-05-23T23:38:48.000Z",
  "updated": "2022-05-23T23:38:48.000Z",
  "title": "Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds",
  "authors": [
    "David Baraglia"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We construct a new family of knot concordance invariants $\\theta^{(q)}(K)$, where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology, constructed by the author and Hekmati, applied to the degree $q$ cyclic cover of $S^3$ branched over $K$. In the case $q=2$, our invariant $\\theta^{(2)}(K)$ shares many similarities with the knot Floer homology invariant $\\nu^+(K)$ defined by Hom and Wu. Our invariants $\\theta^{(q)}(K)$ give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding $K$ in a definite $4$-manifold with boundary $S^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-23T23:38:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K41"
    ],
    "keywords": [
      "knot concordance invariants",
      "slice genus bounds",
      "seiberg-witten theory",
      "knot floer homology invariant",
      "equivariant seiberg-witten-floer cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}