A stable classification of Lefschetz fibrations

Details A stable classification of Lefschetz fibrations A stable classification of Lefschetz fibrations

2004-12-06

arxiv.org/abs/math/0412120v2

Geom. Topol. 9(2005) 203-217

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper6.abs.html

Scientific paper

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.

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