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.
Citation
Weimin Chen. Rostislav Matveyev. "Symplectic Lefschetz fibrations on $S^1 \times M^3$." Geom. Topol. 4 (1) 517 - 535, 2000. https://doi.org/10.2140/gt.2000.4.517
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