Groupes convexes-cocompacts en rang supérieur

Abstract

The convex-cocompact subgroups are central in hyperbolic geometry and more generally in negative curvature. Labourie introduced in 2005 the notion of 'Anosov' subgroup which proves progressively to be the right generalizations of convex-cocompact groups, especially after the works of Kapovich, Leeb and Porti. This expose will review different caracteriations of those groups, emphasizing the parallel (or difference) with the negative curvature, and will give their basic properties.