{
  "id": "math/0210206",
  "version": "v1",
  "published": "2002-10-14T19:29:05.000Z",
  "updated": "2002-10-14T19:29:05.000Z",
  "title": "Families of Simply Connected 4-Manifolds with the Same Seiberg-Witten Invariants",
  "authors": [
    "Ronald Fintushel",
    "Ronald J. Stern"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be distinguished by Seiberg-Witten invariants. Whether these manifolds are, or are not, actually diffeomorphic seems to be a very difficult question to answer. The most interesting of these constructions is a surgery that from certain symplectic 4-manifolds will produce nonsymplectic 4-manifolds. This is detected by calculations of Seiberg-Witten invariants. The surgery in question can be performed on any 4-manifold which contains as a codimension 0 submanifold a punctured surface bundle over a punctured surface and a nontrivial loop in the base which has trivial monodromy. A starting point for another class of examples in this paper is a family of examples which show that the Parshin-Arakelov theorem for holomorphic Lefschetz fibrations is false in the symplectic category. Such families are constructed by means of knot surgery on elliptic surfaces. It is shown that for a fixed homeomorphism type X (of a simply connected elliptic surface) and a fixed integer $g \\ge 3$, there are infinitely many genus g Lefschetz fibrations on nondiffeomorphic 4-manifolds, all homeomorphic to X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-14T19:29:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57"
    ],
    "keywords": [
      "seiberg-witten invariants",
      "elliptic surface",
      "holomorphic lefschetz fibrations",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10206F"
    }
  }
}