Symplectic Lefschetz fibrations on S1 × M3

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

References

Forward citations

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

Volume 4, issue 1 (2000)

Weimin Chen and Rostislav Matveyev