An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle
The group of difisomorphisms of a riemannian manifold of dimension >1 is very “ramified”. The existence of a “reasonnable” quasi invariant measure seems therefore very doubtfull. The case of the group of the diffeomorphisms of the circle S1 is quite different. We shall in this paper identify it with a loop space which carries a natural Wiener measure.
KeywordsCentral Extension Symmetric Operator Loop Space Left Action Wiener Space
Unable to display preview. Download preview PDF.
- M.P. Malliavinet P. Malliavin. Mesures quasi invariantes sur certains groupes de dimension infinie, Note aux C.R. Acad. Sc. Paris, octobre 1990.Google Scholar