Cornelia Vizman

Diffeomorphism groups: central extensions and coadjoint orbits

We construct central extensions of the group of exact volume preserving diffeomorphisms, the universal covering groups of the group of volume preserving diffeomorphisms and of the group of symplectic diffeomorphisms. This is done using infinite dimensional symplectic manifolds (which are also coadjoint orbits for these extensions): (covering spaces of) the non-linear Grassmannian of codimension two submanifolds and the non-linear symplectic Grassmannian of symplectic submanifolds.