Translator Disclaimer
2008 Exotic rational elliptic surfaces without $1$–handles
Kouichi Yasui
Algebr. Geom. Topol. 8(2): 971-996 (2008). DOI: 10.2140/agt.2008.8.971

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

Citation

Download Citation

Kouichi Yasui. "Exotic rational elliptic surfaces without $1$–handles." Algebr. Geom. Topol. 8 (2) 971 - 996, 2008. https://doi.org/10.2140/agt.2008.8.971

Information

Received: 20 September 2007; Accepted: 5 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1161.57017
MathSciNet: MR2443105
Digital Object Identifier: 10.2140/agt.2008.8.971

Subjects:
Primary: 57R55
Secondary: 57N13, 57R57, 57R65

Rights: Copyright © 2008 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.8 • No. 2 • 2008
MSP
Back to Top