Chris Woodward

Lagrangian correspondences in monotone Floer theory and (2+1+1)-d TQFT

Using Floer theory one can define (a) a 2-category whose objects are monotone symplectic manifolds, 1-morphisms are Lagrangian correspondences, and 2-morphisms are Floer homology classes. and (b) a 2-functor which assigns to any monotone symplectic manifold a category, to any Lagrangian correspondence a functor, and to any Floer homology class a natural transformation. Our main result is that composition of functors for Lagrangian correspondences is isomorphic to the functor associated to the geometric composition. As an application, we construct an SU(2) Floer field theory for tangles.