August 2: Morse theory on a manifold with boundary, or: How I learned to stop worrying and love the reducible monopoles

Jonathan Bloom

Now that Tim has done all the hard work of describing the Seiberg-Witten equations, I'll try to motivate the structure of the 3+1 dimensional "TQFT".  I'll start by reviewing Morse theory on a closed manifold, the finite-dimensional model for Floer theory.  I'll then discuss the right way to adapt this story to a manifold with boundary.  The latter serves as the finite-dimensional model for monopole Floer homology, leading to three versions of the theory.