{
  "id": "0705.1143",
  "version": "v1",
  "published": "2007-05-08T19:00:43.000Z",
  "updated": "2007-05-08T19:00:43.000Z",
  "title": "Exotic rational elliptic surfaces without 1-handles",
  "authors": [
    "Kouichi Yasui"
  ],
  "comment": "19 pages, 41 figures",
  "journal": "Algebraic & Geometric Topology 8 (2008), no. 2, 971-996",
  "categories": [
    "math.GT"
  ],
  "abstract": "Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as $E(1)_{2,3}$ and admits neither 1- nor 3-handles, by using rational blow-downs and Kirby calculus. Our manifold gives the first example of either a counterexample to the Harer-Kas-Kirby conjecture or a homeomorphic but non-diffeomorphic pair of simply connected closed smooth 4-manifolds with the same non-vanishing Seiberg-Witten invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-08T19:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R65",
      "57R57",
      "57N13"
    ],
    "keywords": [
      "exotic rational elliptic surfaces",
      "harer-kas-kirby conjecture",
      "handle decomposition",
      "first example",
      "non-vanishing seiberg-witten invariants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.1143Y"
    }
  }
}