Exotic rational elliptic surfaces without 1-handles
Geometric Topology
2016-01-20 v1
Abstract
Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as 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.
Cite
@article{arxiv.0705.1143,
title = {Exotic rational elliptic surfaces without 1-handles},
author = {Kouichi Yasui},
journal= {arXiv preprint arXiv:0705.1143},
year = {2016}
}