Exotic rational elliptic surfaces without 1–handles

Yasui, Kouichi¹

¹Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 971-996

Résumé

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 nondiffeomorphic pair of simply connected closed smooth 4–manifolds with the same nonvanishing Seiberg–Witten invariants.

Détail

DOI : 10.2140/agt.2008.8.971

Keywords: Kirby calculus, rational blow-down, 1-handle, Seiberg–Witten invariant, small exotic 4-manifold

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