STRATIFIED SYMPLECTIC SPACES AND REDUCTION
成果类型：
Article
署名作者：
SJAMAAR, R; LERMAN, E
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/2944350
发表日期：
1991
页码：
375-422
关键词：
摘要：
Let (M, omega) be a Hamiltonian G-space with proper momentum map J: M --> g*. It is well-known that if zero is a regular value of J and G acts freely on the level set J-1(0), then the reduced space M0 : = J-1(0)/G is a symplectic manifold. We show that if the regularity assumptions are dropped, the space M0 is a union of symplectic manifolds; i.e., it is a stratified symplectic space. Arms et al. [2] proved that M0 possesses a natural Poisson bracket. Using their result, we study Hamiltonian dynamics on the reduced space. In particular we show that Hamiltonian flows are strata-preserving and give a recipe for lifting a reduced Hamiltonian flow to the level set J-1(0). Finally we give a detailed description of the stratification of M0 and prove the existence of a connected open dense stratum.