Brendan Owens, McMaster University, December 2, 2002

Title: Floer homology of a surface times a circle using Bott-Morse theory

Abstract:

I will describe a generalised Morse complex which computes the homology groups of a manifold M from a Bott-Morse function on M. There is a version of this by Fukaya for instanton Floer homology. I will explain how this gives a new and simpler proof that the Floer homology of a surface times a circle is isomorphic to the homology of the moduli space of projectively flat connections on the surface. (This was first proved by Dostoglou and Salamon using an adiabatic limit argument and results of Floer on symplectic Floer homology).