October 27, 2006

Stefano Vidussi (UC Riverside)

Title: Symplectic $S^1 \times N^3$ and subgroup separability

Abstract: In this talk I will discuss some results related to the conjecture that a 4-manifold of the form $S^1 \times N^3$ admits a symplectic structure if and only if $N$ fibers over the circle. In particular, I will show that the conjecture holds true if the fundamental group of $N$ satisfies suitable subgroup separability conditions. For example, this leads to a complete solution for the case where $N$ has vanishing Thurston norm (e.g., when obtained by $0$-surgery on a genus-$1$ knot). (Joint work with Stefan Friedl.)