Special Topology Seminar - Guillem Cazassus - Extending down Donaldson-Floer theory
Title: Extending down Donaldson-Floer theory
Abstract: The Donaldson polynomials are powerful invariants in Low Dimensional Topology: for example they are able to distinguish smooth manifolds that are homeomorphic, but not diffeomorphic. They are rooted in theoretical physics (Yang-Mills gauge theory) and are difficult to compute, as they involve solving a PDE (the Anti-Self-Dual equation).
I will present a program aimed at computing these by "cut-and-paste" operations. Specifically I will explain how to recast these into an "extended Topological Field Theory". This will involve going from
Gauge Theory to Symplectic Geometry, Hamiltonian actions and Homotopical Algebra.