The Fukaya category of a fibration with singularities W : M→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.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
