Coisotropic embeddings in Poisson manifolds

Details Coisotropic embeddings in Poisson manifolds Coisotropic embeddings in Poisson manifolds

2006-11-15

arxiv.org/abs/math/0611480v4

Transactions A.M.S., Vol. 361 (2009), pp. 3721-3746

Mathematics

Symplectic Geometry

Several proofs have been shortened and simplified. Final version, to appear in Trans. A.M.S. 24 pages

Scientific paper

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.

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