T. Mrowka (M.I.T.)
"Floer homology for Seiberg-Witten monopoles"

Contents.

This course will cover the construction of various
versions of Floer homology for Seiberg-Witten monopoles.
We will begin with a discussion of finite dimensional
Morse theory focusing on the how the usual construction
needs to be modified to deal with a function
invariant under circle action. Then we will discuss
the monopole equations on three and four dimensional
manifolds and indicate how the Chern-Simons-Dirac
function compares with the finite dimensional situation.
We will discuss many of the details needed to rigorously
construct the Morse complex: transversality, compactness
and glueing. As time permits we will describe how these groups
facilitate computations of the Seiberg-Witten invariants
and discuss the surgery long exact sequence.