Key points are not available for this paper at this time.
Atiyah and Bott pointed out, in This observation, together with various extensions, has stimulated a great deal of work and provides a conceptual framework to understand many phenomena in Yang-Mills theory. Our purpose in this paper is to explore some similar ideas in the framework of diffeomorphism groups. We begin by identifying a moment map in a rather general setting, and then see how the ideas work in some more specific situations. We hope to show that the moment map point of view is useful, both in understanding certain established results and also in suggesting new problems in geometry and analysis. While these analytical questions are the main motivation for the work, we will concentrate here on the formal aspects and will not make any serious inroads on the analysis.
Simon Donaldson (Fri,) studied this question.