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Regular Reduction by Stages

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1913)

In this chapter we formulate the first of several reduction by stages theorems in the regular, that is, free actions, case. We state a sufficient condition, called the stages hypothesis under which the two step reduced space is symplectically diffeomorphic to the space obtained by reducing all at once by the original group. In Chapters 11 and 12 we will come up with alternative conditions for reduction by stages based on the use of distribution theory.

Keywords

  • Normal Subgroup
  • Heisenberg Group
  • Symplectic Form
  • Symplectic Manifold
  • Semidirect Product

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Regular Reduction by Stages. In: Hamiltonian Reduction by Stages. Lecture Notes in Mathematics, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72470-4_5

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