A stable classification of Lefschetz fibrations

Auroux, Denis

doi:10.2140/gt.2005.9.203

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A stable classification of Lefschetz fibrations

Denis Auroux

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 $f_{g}^{0}$ with the property that, if two Lefschetz fibrations over $S^{2}$ 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 $f_{g}^{0}$ they become isomorphic. As a consequence, any two compact integral symplectic 4–manifolds with the same values of $(c_{1}^{2}, c_{2}, c_{1} \cdot [ω], {[ω]}^{2})$ become symplectomorphic after blowups and symplectic sums with $f_{g}^{0}$ .

Keywords

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

Mathematical Subject Classification 2000

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

Denis Auroux
Department of Mathematics MIT Cambridge Massachusetts 02139 USA

Volume 9, issue 1 (2005)