Geometry & Topology

A stable classification of Lefschetz fibrations

Denis Auroux

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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

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

Received: 7 December 2004
Accepted: 18 January 2005
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

symplectic 4–manifolds Lefschetz fibrations fiber sums mapping class group factorizations


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

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