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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© 2004 Juan Pablo Ortega and Tudor S. Ratiu
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Ortega, JP., Ratiu, T.S. (2004). The Symplectic Slice Theorem. In: Momentum Maps and Hamiltonian Reduction. Progress in Mathematics, vol 222. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-3811-7_7
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DOI: https://doi.org/10.1007/978-1-4757-3811-7_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-3813-1
Online ISBN: 978-1-4757-3811-7
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