Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds.
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Dans cet article, nous étudions le flot des chambres de Weyl d’une large classe de sous-groupe discrets d’un groupe de Lie semi-simple réel : les groupes de Ping-Pong. Nous montrons que ce flot est mélangeant relativement à la mesure de Patterson-Sullivan ; celle-ci étant infinie en rang , nous précisons cette propriété de mélange en explicitant sa vitesse dans le direction du vecteur de croissance du groupe.