Exotic rational elliptic surfaces without 1-handles

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.

19 pages, 41 figures

References in corpus (5)

• Simply connected symplectic 4-manifolds with $b_2^{+}=1$ and $c_1^2=2$
• An exotic smooth structure on CP^2+6CP^2-bar
• Exotic rational elliptic surfaces without 1-handles
• Symplectic tori in rational elliptic surfaces
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Cited by in corpus (8)

• Corks, Plugs and exotic structures
• Exotic rational elliptic surfaces without 1-handles
• Stein 4-manifolds and corks
• Knotting corks
• Geometrically simply connected 4-manifolds and stable cohomotopy Seiberg-Witten invariants
• Elliptic surfaces without 1-handles
• Small exotic rational surfaces without 1- and 3-handles
• Small exotic Stein manifolds