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 blowdowns 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. © 2008 Algebraic & Geometric Topology.