Geometry & Topology

A stable classification of Lefschetz fibrations

Denis Auroux

Abstract

We study the classification of Lefschetz fibrations up to stabilization by fiber sum operations. We show that for each genus there is a “universal” fibration $fg0$ with the property that, if two Lefschetz fibrations over $S2$ have the same Euler–Poincaré characteristic and signature, the same numbers of reducible singular fibers of each type, and admit sections with the same self-intersection, then after repeatedly fiber summing with $fg0$ they become isomorphic. As a consequence, any two compact integral symplectic 4–manifolds with the same values of $(c12,c2,c1⋅[ω],[ω]2)$ become symplectomorphic after blowups and symplectic sums with $fg0$.

Article information

Source
Geom. Topol., Volume 9, Number 1 (2005), 203-217.

Dates
Accepted: 18 January 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799564

Digital Object Identifier
doi:10.2140/gt.2005.9.203

Mathematical Reviews number (MathSciNet)
MR2115673

Zentralblatt MATH identifier
1084.57024

Citation

Auroux, Denis. A stable classification of Lefschetz fibrations. Geom. Topol. 9 (2005), no. 1, 203--217. doi:10.2140/gt.2005.9.203. https://projecteuclid.org/euclid.gt/1513799564

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