On the classification of the coadjoint orbits of the Sobolev Bott–Virasoro group

The purpose of this paper is to give the classification of the Bott–Virasoro coadjoint orbits, with nonzero central charge, in the functional analytic setting of smooth Hilbert manifolds. The central object of the paper is thus the completion of the Bott–Virasoro group with respect to a Sobolev topology, giving rise to a smooth Hilbert manifold and topological group, called the Sobolev Bott–Virasoro group. As a consequence of this approach, analytic and geometric properties of the coadjoint orbits are studied.