Optimal Reduction

  • Juan-Pablo Ortega
  • Tudor S. Ratiu
Part of the Progress in Mathematics book series (PM, volume 222)


In this chapter we use the optimal momentum map introduced in Chapter 5 to carry out symplectic reduction. The reduced spaces that we will obtain generalize the symplectic strata presented in Chapter 8 to the categories in which the optimal momentum map is well defined. More specifically, the optimal momentum map approach allows the construction of symplectic point and orbit reduced spaces purely within the Poisson category under hypotheses that do not necessarily imply the existence of a standard momentum map.


Symplectic Form Symplectic Manifold Symplectic Structure Isotropy Subgroup Polar Distribution 
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Copyright information

© Juan Pablo Ortega and Tudor S. Ratiu 2004

Authors and Affiliations

  • Juan-Pablo Ortega
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.CNRS-Laboratoire de Mathématiques de BensançonUniversité de Franche-Comté, UFR des Sciences et TechniquesBensançon CedexFrance
  2. 2.Départment de MathématiquesLausanneSwitzerland

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