Some remarks on area-preserving actions of lattices

In the spirit of Zimmer’s study of large groups actions on closed manifolds, we discuss the existence of area-preserving actions of higher rank lattices on surfaces. We explain why certain vanishing results in bounded cohomology, due to Burger and Monod, combined with some constructions by Gambaudo and Ghys, give some con-straints on the measure theoretical properties of such actions.