Symplectic Lefschetz fibrations on S^1 x M^3

TL;DR

This paper classifies symplectic Lefschetz fibrations on four-manifolds formed by the product of a three-manifold and a circle, supporting a conjecture about their symplectic structures and fiberings.

Contribution

It provides a classification of symplectic Lefschetz fibrations on S^1 x M^3, offering evidence for a conjecture relating symplectic structures to three-manifold fibrations.

Findings

Classified symplectic Lefschetz fibrations on S^1 x M^3.

Supports conjecture linking symplectic structures to three-manifold fibrations.

Shows symplectic structures are deformation equivalent to canonical structures.

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.