Singular Poisson Reduction of Cotangent Bundles

Abstract

We consider the Poisson reduced space (T Q)/K , where the action of the com pact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T Q. Realizing (T Q)/K as a Weinstein space we deter mine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q Q/K which are of single orbit type.