Groupes de Neretin et propriété (T) de Kazhdan

We consider Neretin's group of boundary extensions of piecewise isometries of a homogeneous simplicial tree. We prove that if a subgroup Γ of this group has Kazhdan's property (T), then a finite index subgroup of Γ stabilizes a finite collection of balls of the boundary of the tree, acting isometrically on each of them. To cite this article: A. Navas, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 789–792.