Poisson geometry around Poisson submanifolds

Abstract

We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases all the known linearization theorems for fixed points and symplectic leaves. The symplectic groupoid version of these results gives a solution to the groupoid coisotropic embedding problem.

75 pages; several improvements in the exposition, with two sections moved to appendices; conventions for algebroids/groupoids were changed. Final version accepted for publication in JEMS