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Commutators and diffeomorphisms of surfaces. (English) Zbl 1088.37018
Summary: For any compact oriented surface $$\Sigma$$, we consider the group of diffeomorphisms of $$\Sigma$$ which preserve a given area form. 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.

##### MSC:
 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37C05 Dynamical systems involving smooth mappings and diffeomorphisms 57M60 Group actions on manifolds and cell complexes in low dimensions 20F28 Automorphism groups of groups
##### Keywords:
area-preserving diffeomorphisms; quasi-morphisms
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