The topology of Hamiltonian Loop Group spaces
Northeastern University, U.S.A.
We study Morse theory on Hamiltonian Loop Group spaces with proper moment map. We show that as for compact manifolds, the square of the moment map gives a perfect Morse-Bott decomposition of such a space. Two examples are the space of based loops on a Lie Group (where the Morse function is the Energy function of Morse and Bott) and a space closely related to the space of connections on a two-manifold (where the reduced space is the moduli of stable bundles on a Riemann surface). As an application, we give a simple computation of the Poincare series of the moduli of stable bundles.
(joint work with R. Bott and S. Tolman)