SEMINÁRIO SIMPLÉTICO - Contact groupoid actions and their dual pairs

Contact groupoid actions and their dual pairs
Expositor: Maria Amélia Salazar
Instituição: UFF
Data e Horário: 28/09/18 | 14:00h

RESUMO: Contact groupoid actions appear as a natural (and much richer) generalization of contact group actions. As in the symplectic case, where much of the geometry of a symplectic manifold with a Hamiltonian action is encoded in the Hamiltonian moment map to the dual of the Lie algebra, in contact geometry a contact manifold with a contact group gives rise to a (Hamiltonian version of the moment) map with target the projectivization of the dual of the Lie algebra -- a Jacobi manifold which plays the role of the linear Poisson structure of the dual of a Lie algebra, in the context of Jacobi geometry -- and much of the contact geometry is encoded in this map. Contact groupoid actions fits in the setting of contact dual pairs, and this gives a nice explanation of the relation of the contact geometry and the moment maps.