Commutators and diffeomorphisms of surfaces

2004

For any compact oriented surfacewe consider the group of diffeomorphisms ofwhich preserve a given area form. In this paper we show that the vector space of homogeneous quasi-morphisms on this group has infinite dimension. This result is proved by constructing explicitly and for each surface an infinite family of independent homogeneous quasi-morphisms. These constructions use simple arguments related to linking properties of the orbits of the diffeomorphisms.