Surjectivity for Hamiltonian loop group spaces
成果类型：
Article
署名作者：
Bott, R; Tolman, S; Weitsman, J
署名单位：
Harvard University; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Santa Cruz
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-003-0319-2
发表日期：
2004
页码：
225-251
关键词：
摘要：
Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,omega) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,omega), and assume that the moment map mu:X-->Lg(*) is proper. We consider the function |mu|(2):X-->R, and use a version of Morse theory to show that the inclusion map j:mu(-1)(0)-->X induces a surjection j(*):H-G(*)(X)-->H-G(*)(mu(-1)(0)), in analogy with Kirwan's surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces.
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