A characteristic class of Hamiltonian fibrations and a group cocycle

In this talk, I will introduce two cohomology classes. The first one is a third group cohomology class that is analogous to the one introduced by R.S. Ismagilov, M. Losik, and P.W. Michor in 2006. This class is given as a group cocycle of the symplectic diffeomorphism group. The second one is a characteristic class of Hamiltonian fibrations, which is defined by using the Serre spectral sequence. This characteristic class is related to the prequantization of Hamiltonian fibrations. I will introduce the constructions and properties of these classes, and after that, explain how they relate.