Geometry & Topology
- Geom. Topol.
- Volume 9, Number 1 (2005), 203-217.
A stable classification of Lefschetz fibrations
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 with the property that, if two Lefschetz fibrations over 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 they become isomorphic. As a consequence, any two compact integral symplectic 4–manifolds with the same values of become symplectomorphic after blowups and symplectic sums with .
Geom. Topol., Volume 9, Number 1 (2005), 203-217.
Received: 7 December 2004
Accepted: 18 January 2005
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R17: Symplectic and contact topology
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Auroux, Denis. A stable classification of Lefschetz fibrations. Geom. Topol. 9 (2005), no. 1, 203--217. doi:10.2140/gt.2005.9.203. https://projecteuclid.org/euclid.gt/1513799564