Coadjoint orbits of the group of contact diffeomorphisms
Speaker: Cornelia Vizman, West University of Timisoara.
Date: 20 sep 2019, 11h.
Place: Room 407, Bloco H, Campus Gragoatá, UFF.
Abstract: (Joint work with Stefan Haller from the University of Vienna) Generalizing the canonical symplectization of contact manifolds, we construct an infinite dimensional manifold of weighted embeddings into a contact manifold. This space carries a symplectic structure such that the contact group and the group of reparametrizations act in a Hamiltonian fashion with equivariant moment maps, respectively, giving rise to a dual pair, called the EPContact dual pair. Via symplectic reduction, it provides a conceptual identification of nonlinear Grassmannians of weighted isotropic submanifolds of the contact manifold with certain coadjoint orbits of the contact group. For the projectivized cotangent bundle, the EPContact dual pair is closely related to the EPDiff dual pair due to Holm and Marsden, and leads to a geometric description of some coadjoint orbits of the full diffeomorphism group.