Submanifolds in poisson geometry: A survey

Abstract

We describe various classes of submanifolds of a Poisson manifold M, both in terms of tensors on M and of constraints: coisotropic submanifolds, Poisson- Dirac submanifolds (which inherit a Poisson structure), and the very general class of pre-Poisson submanifolds. We discuss embedding results for these classes of submanifolds, quotient Poisson algebras associated to them, and their relationship to subgroupoids of the symplectic groupoid of M. © Springer-Verlag Berlin Heidelberg 2011.