Wrapped Floer theory on Liouville sectors

John Pardon, Princeton University
Fine Hall 314

I will introduce the basics of wrapped Floer homology.  In two dimensions, this involves drawing simple pictures, though becomes more complicated in higher dimensions.  Usually wrapped Floer theory takes place on certain non-compact symplectic manifolds, for example a complex submanifold of C^n, or (the total space of) a cotangent bundle of a compact manifold.  In joint work with Sheel Ganatra and Vivek Shende, we introduce a larger class of symplectic manifolds (this time with boundary), called Liouville sectors, on which wrapped Floer theory makes sense.  I will explain how one can use this formalism to study wrapped Floer on many Liouville manifolds by decomposing them into simpler Liouville sectors.