A note on the geometry of M-3 and symplectic structures on S-1 x M-3

Abstract

We investigate the relationship between the geometry of a closed, oriented 3-manifold M and the symplectic structures on S-1 x M. In most cases the existence of a symplectic structure on S-1 x M and Thurston's geometrization conjecture imply the existence of a geometric structure on M. This observation together with the existence of geometric structures on most 3-manifolds which fiber over the circle suggests a different approach to the problem of finding a fibration of a 3-manifold over the circle in case its product with the circle admits a symplectic structure.