Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A stable classification of Lefschetz fibrations

Denis Auroux

Geometry & Topology 9 (2005) 203–217

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 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.

Keywords
symplectic 4–manifolds, Lefschetz fibrations, fiber sums, mapping class group factorizations
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D35
References
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Publication
Received: 7 December 2004
Accepted: 18 January 2005
Published: 20 January 2005
Proposed: Tomasz Mrowka
Seconded: Ronald Fintushel, Ronald Stern
Authors
Denis Auroux
Department of Mathematics
MIT
Cambridge
Massachusetts 02139
USA