Chennai Mathematical Institute

Seminars




2.00 p.m.
The topology of Hamiltonian Loop Group spaces

Jonathan Weitsman
Northeastern University, U.S.A.
19-01-12


Abstract

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)





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