Geometry & Topology, Vol. 9 (2005) Paper no. 6, pages 203--217.

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 f^0_g with the property that, if two Lefschetz fibrations over S^2 have the same Euler-Poincare 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 f^0_g they become isomorphic. As a consequence, any two compact integral symplectic 4-manifolds with the same values of (c_1^2, c_2, c_1.[w], [w]^2) become symplectomorphic after blowups and symplectic sums with f^0_g.

Keywords. Symplectic 4-manifolds, Lefschetz fibrations, fiber sums, mapping class group factorizations

AMS subject classification. Primary: 57R17. Secondary: 53D35.

DOI: 10.2140/gt.2005.9.203

E-print: arXiv:math.GT/0412120

Submitted to GT on 7 December 2004. Paper accepted 18 January 2005. Paper published 20 January 2005.

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Denis Auroux
Department of Mathematics, MIT
Cambridge MA 02139, USA

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