Seminarium Gamma

Symplectic foliations are foliations where every leave carries a symplectic form. They are the same thing as regular Poisson structures.Given a symplectic foliation, we construct an algebraic structure that “governs” its deformations. This will allow, for instance, to find first order deformations of a regular Poisson manifold that can be extended to a path of Poisson structures, but not to a path of regular Poisson structures. We will also related deformations of symplectic foliations to those of the underlying foliations.The main geometry tool we use are Dirac structures, which provide a convenient generalization of Poisson structures.