The Symplectic Slice Theorem
Most of the good technical behavior of proper Lie group actions is a direct consequence of the existence of slices and tubes; they provide a privileged system of semiglobal coordinates in which the group action takes on a particularly simple form. Proper symplectic Lie group actions turn out to behave similarly: the tubular chart can be constructed in such a way that the expression of the symplectic form is very natural and, moreover, if there is a momentum map associated to this canonical action, this construction provides a normal form for it. The statement and proof of this Symplectic Slice Theorem is the main goal of this chapter.
KeywordsSymplectic Form Symplectic Manifold Horizontal Lift Horizontal Curve Lagrangian Subspace
Unable to display preview. Download preview PDF.