Avviso di seminario

Venerdì 22 novembre, alle ore 12, in aula G, il prof. Konstantinos Efstathiou, della Duke-Kunshan University (Kunshan, Jiangsu, Cina), terrà un seminario dal titolo: "Maslov circle bundles".

Sunto

We introduce the Maslov S^1 bundles over symplectic manifolds (M, ω), that is, the determinant bundle Γ of the unitary frame bundle over M, and the bundle Γ^2 = Γ / {±1}. The usual Maslov index is defined when the bundles are trivial. We discuss the properties of the Maslov bundles focusing on the interplay between their geometry and the dynamics of symplectic group actions on M. Symplectic group actions can be lifted to group actions on the Maslov bundles. When M is a homogeneous G-space, then so are Γ and Γ^2. Moreover, we provide an alternative proof of the fact that when M is a monotone symplectic manifold then the symplectic action is Hamiltonian. Finally, in the particular case of symplectic circle actions, we define the notion of Maslov data which generalizes the notion of Maslov index to the case where the Maslov bundle is not trivial.