The purpose of this introductory Chapter is to both establish basic notation and also to give a reasonably complete account of symplectic reduction theory. The first section is a basic introduction, the second provides proofs and the third gives a history of the subject. This chapter focuses on reduction theory in the general setting of symplectic manifolds. The next chapter deals with, amongst other things, the important case of cotangent bundle reduction. Both of these cases are fundamental ingredients in the reduction by stages program.
Keywords
- Symplectic Form
- Symplectic Manifold
- Cotangent Bundle
- Nonholonomic System
- Reduction Theory
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Symplectic Reduction. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_1
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DOI: https://doi.org/10.1007/978-3-540-72470-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72469-8
Online ISBN: 978-3-540-72470-4
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