Nombre de rotation, structures géométriques sur un cercle et groupe de Bott-Virasoro

Abstract

A complete classification of coadjoint stabilizers of the Bott-Virasoro group is obtained via an essentially geometrical method. The basic tool is the rotation number of a diffeomorphism of the circle. In particular, we find non-connected isotropy groups and show that the Miura transformation of Hill’s operators can be seen as a moment map on the space of affine structures on the circle.