Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

We study the Hamiltonian group of a symplectic manifold, satisfying some mild additional assumptions, by means of the associated quantomorphism group. Recall that, according to Souriau, the quantomorphism group is the strict contactomorphism group of the total space of a prequantization bundle over the manifold in question. Our investigations are concentrated on the problem of estimations (from below) of the Hofer metric on the Hamiltonian group. We establish the unboundedness of the metric and its non-degeneracy using contact geometry instead of hard symplectic methods known from the literature.