#### 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.

Notes on file formats
Denis Auroux

Department of Mathematics, MIT

Cambridge MA 02139, USA

Email: auroux@math.mit.edu

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