The role of Poisson transversals in Poisson geometry is analogous to the one played by symplectic submanifolds in symplectic geometry, and by transverse submanifolds in foliation theory. They are defined as submanifolds that intersect the symplectic leaves transversally and symplectically.
I will talk about the geometry of the infinite dimensional manifold of compact Poisson transversals. In particular, for unimodular Poisson structures, this space carries a symplectic structure. This construction generalizes and was much inspired by the construction of the symplectic Grassmannian introduced by Stefan Haller and Cornelia Vizman.
This is joint work with Pedro Frejlich.
(Séminaire Physmath)