A stable classification of Lefschetz fibrations

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.