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.
Unable to display preview. Download preview PDF.