Quasi-morphisme de Calabi sur les surfaces de genre supérieur

Abstract

We construct a homogeneous quasi-morphism Cal S on the group of Hamiltonian diffeomorphisms of a (closed, connected, oriented) surface S of genus greater or equal to 2, with the following property. For each connected open set U in S diffeomorphic to a disk or to an annulus, the restriction of Cal S to the subgroup of diffeomorphisms which are the time 1 map of a Hamiltonian isotopy in U, equals Calabi's homomorphism. To cite this article: P. Py, C. R. Acad. Sci. Paris, Ser. I 341 (2005).