Topology Seminar (Main Talk): Distinguishing fillings using dynamics of Fukaya categories

Seminar | October 3 | 4-5 p.m. | 3 Evans Hall

 Yusuf Baris Kartal, MIT

 Department of Mathematics

One can construct the open symplectic mapping torus \(T_\phi \) for a given a Weinstein manifold \(M\) and a compactly supported symplectomorphism \(\phi \). Its contact boundary is independent of \(\phi \) and is equal to contact boundary of \(T_0\times M\) where \(T_0\) is the torus with a small ball removed. In this talk, we will outline a method to distinguish the fillings \(T_\phi \) and \(T_0\times M\). We will exploit the dynamics and deformation theory of the (wrapped) Fukaya categories, where the dynamics of the same sort is invisible at a geometric level.