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.