{
  "id": "1510.07715",
  "version": "v1",
  "published": "2015-10-26T23:02:03.000Z",
  "updated": "2015-10-26T23:02:03.000Z",
  "title": "Fintushel--Stern knot surgery in torus bundles",
  "authors": [
    "Yi Ni"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Suppose that $X$ is a torus bundle over a closed surface with homologically essential fibers. Let $X_K$ be the manifold obtained by Fintushel--Stern knot surgery on a fiber using a knot $K\\subset S^3$. We prove that $X_K$ has a symplectic structure if and only if $K$ is a fibered knot. The proof uses Seiberg--Witten theory and a result of Friedl--Vidussi on twisted Alexander polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T23:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "57M50",
      "57M10"
    ],
    "keywords": [
      "fintushel-stern knot surgery",
      "torus bundle",
      "symplectic structure",
      "seiberg-witten theory",
      "twisted alexander polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007715N"
    }
  }
}