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Moments and reductions

II. Symplectic Geometry

Part of the Lecture Notes in Mathematics book series (LNM,volume 905)

Abstract

In this note we gather together some diverse facts about the moment map for symplectic group actions and the corresponding reductions of the symplectic manifold on which the group acts. We also relate moment maps with the “character Lagrangian” so as to obtain “intertwining Lagrangians” for Hamiltonian group actions.

Keywords

  • Symplectic Form
  • Symplectic Manifold
  • Lagrangian Submanifold
  • Connected Subgroup
  • Hamiltonian Action

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References

  1. Abraham, R. and Marsden, J., Foundations of Mechanics 2nd Edit. Benjamin/Cummings Pub. Co. Reading, Mass. 1978 Ex. 5. 31, page 422.

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© 1982 Springer-Verlag Berlin Heidelberg

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Guillemin, V., Sternberg, S. (1982). Moments and reductions. In: Doebner, HD., Andersson, S.I., Petry, H.R. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092427

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  • DOI: https://doi.org/10.1007/BFb0092427

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11197-9

  • Online ISBN: 978-3-540-39002-2

  • eBook Packages: Springer Book Archive