Geometry & Topology 9 (2005) 203–217

DOI: 10.2140/gt.2005.9.203

arXiv: math.GT/0412120

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 f⁰_g 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 f⁰_g 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 f⁰_g.

Keywords

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

Mathematical Subject Classification

Primary: 57R17

Secondary: 53D35

References

Forward citations

Publication

Received: 7 December 2004
Accepted: 18 January 2005
Published: 20 January 2005
Proposed: Tomasz Mrowka
Seconded: Ronald Fintushel, Ronald Stern

Authors