Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface E(1)2,3 requires both 1and 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 1nor 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 4â€¦Â CONTINUE READING

An exotic rational elliptic surfaces without 1- or 3-handles, to appear in the proceedings of the international conference, â€œIntelligence of Low Dimensional Topology 2006

K. Yasui

World Scientific Publishing Co. in the Knots and Everything Book Series â€¢ 2006