# Connectivity properties of moment maps on based loop groups

@article{Harada2006ConnectivityPO,
title={Connectivity properties of moment maps on based loop groups},
author={Megumi Harada and Tara S. Holm and Lisa C. Jeffrey and A. L. Mare},
journal={Geometry \& Topology},
year={2006},
volume={10},
pages={1607-1634}
}
• Published 29 March 2005
• Mathematics
• Geometry & Topology
For a compact, connected, simply-connected Lie group G, the loop group LG is the infinite-dimensional Hilbert Lie group consisting of H^1-Sobolev maps S^1-->G. The geometry of LG and its homogeneous spaces is related to representation theory and has been extensively studied. The space of based loops Omega(G) is an example of a homogeneous space of $LG$ and has a natural Hamiltonian T x S^1 action, where T is the maximal torus of G. We study the moment map mu for this action, and in particular…
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