Tobias Ekholm: Duality between Legendrian and Lagrangian invariants

Abstract:
We discuss Floer cohomological dualities for exact Lagrangian fillings of Legendrian submanifolds in the boundary of a Weinstein manifold (exact symplectic manifold with contact boundary). The dualities are counterparts of dualities between a manifold and its loop space in algebraic topology, the Floer cohomology of the Lagrangian filling plays the role of chains on the manifold and the Chekanov-Eliashberg dg-algebra of the Legendrian boundary plays the role of the chains on the based loop space.