# Symplectic Topology Seminar

Title: Simple homotopy equivalence of nearby Lagrangians.
Abstract: I will start by outlining the main ideas involved in defining the Fukaya category of the cotangent bundle of a smooth closed manifold Q. This (roughly) has objects given by exact Lagrangians in T*Q. I will then recall the notion of Whitehead torsion for a homotopy equivalence of finite CW complexes and explain how to make sense of this notion for en equivalence between two exact Lagrangians in the Fukaya category. I will then sketch how a certain filtration argument proves that in this Fukaya category this notion is trivial - proving that all exact Lagrangians in the cotangent bundle is in fact simple homotopy equivalent to Q. This is joint work with M. Abouzaid.