A criterion for generating Fukaya categories of fibrations

Princeton/IAS Symplectic Geometry Seminar
Topic:A criterion for generating Fukaya categories of fibrations
Speaker:Sheel Ganatra
Affiliation:Stanford University
Date:Friday, February 21
Time/Room:1:30pm - 2:30pm/S-101
Video Link:https://video.ias.edu/pisgs/2014/0221-SheelGanatra

The Fukaya category of a fibration with singularities \(W: M \to C\), or Fukaya-Seidel category, enlarges the Fukaya category of \(M\) by including certain non-compact Lagrangians and asymmetric perturbations at infinity involving \(W\); objects include Lefschetz thimbles if \(W\) is a Lefschetz fibration. I will recall this category and then explain a criterion, in the spirit of work of Abouzaid and Abouzaid-Fukaya-Oh-Ohta-Ono, for when a finite collection of Lagrangians split-generates such a fibration. The new ingredients needed include a Floer homology group associated to \((M,W)\) and the Serre functor. This is work in progress with Mohammed Abouzaid.