6533b85dfe1ef96bd12bdbe1

RESEARCH PRODUCT

Commutators and diffeomorphisms of surfaces

Jean-marc GambaudoÉTienne Ghys

subject

Surface (mathematics)Pure mathematicsDimension (vector space)Simple (abstract algebra)HomogeneousGroup (mathematics)Applied MathematicsGeneral MathematicsMathematical analysisMathematicsVector space

description

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.

yearjournalcountryeditionlanguage
2004-10-01Ergodic Theory and Dynamical Systems
https://doi.org/10.1017/s0143385703000737