Abstract
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.
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