Singular reduction of Poisson manifolds

The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu . In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits crea ted by a Hamiltonian Lie group action, one reproduces the Universal Reducti on Procedure of Arms, Cushman, and Gotay. Mathematics Subject Classificatio ns (1991): 70H33, 58F05, 53C80.