Déformations de réseaux dans certains groupes résolubles

Abstract

We aim to study local rigidity and deformations for the following class of groups: the semidirect product Γ= Z n ⋊ A Z where n≥2 is an integer and A is a hyperbolic matrix in SL( n,Z ) , considered first as a lattice in the solvable Lie group G= R n ⋊ A R , then as a subgroup of the semisimple Lie group SL( n+1,R ) . We will notably show that, although Γ is locally rigid neither in G nor in H , it is locally SL( n+1,R ) -rigid in G in the sense that every small enough deformation of Γ in G is conjugated to Γ by an element of SL( n+1,R ) .