#### Volume 4, issue 1 (2000)

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Symplectic Lefschetz fibrations on $S^1 \times M^3$

### Weimin Chen and Rostislav Matveyev

Geometry & Topology 4 (2000) 517–535
 arXiv: math.DG/0002022
##### Abstract

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.

##### Keywords
4–manifold, symplectic structure, Lefschetz fibration, Seiberg–Witten invariants
##### Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57R17, 57R57
##### Publication
Received: 12 April 2000
Revised: 8 December 2000
Accepted: 17 December 2000
Published: 21 December 2000
Proposed: Dieter Kotschick
Seconded: Robion Kirby, Yasha Eliashberg
##### Authors
 Weimin Chen University of Wisconsin at Madison Madison Wisconsin 53706 USA Rostislav Matveyev SUNY at Stony Brook Stony Brook New York 11794 USA