Tolga Etgu, McMaster University, September 30, 2002

Title: Symplectic structures on S^1 \times M^3 and the fibrations of M over S^1

Abstract:

If a closed 3-manifold $M$ fibers over the circle, then $S^1 \times M$ admits a symplectic structure. It is conjectured by Cliff Taubes that the converse of this statement is also true. A special case of this conjecture (where the symplectic structure on $S^1 \times M$ is compatible with a Lefschetz fibration) was proved by Weimin Chen and Slava Matveyev. It is possible to get rid of the compatibility condition and also possible to show that the conjecture holds in some other special cases: when $S^1 \times M$ admits a complex structure or a Seifert fibration. We will discuss the conjecture and these partial results.