Abstract
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.
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Bibliography
H. Airault et P. Malliavin. Intégration géométrique sur l’espace de Wiener, Bull. Se. Math., 112, 1988, 3–52.
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M.P. Malliavinet P. Malliavin. Mesures quasi invariantes sur certains groupes de dimension infinie, Note aux C.R. Acad. Sc. Paris, octobre 1990.
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© 1991 Springer-Verlag Tokyo
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Malliavin, M.P., Malliavin, P. (1991). An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle. In: Kashiwara, M., Miwa, T. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68170-0_12
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DOI: https://doi.org/10.1007/978-4-431-68170-0_12
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