Stability of discontinuous groups for reduced threadlike Lie groups

Abstract

Let G be a reduced threadlike Lie group, H an arbitrary closed connected subgroup of G and Γ ⊂ G an abelian discontinuous subgroup for G/H. We study in this work some topological properties of the parameter space [Formula: see text] and the deformation space [Formula: see text], namely the stability and the rigidity. Instead of treating stability, we consider a weaker form by using an explicit covering of Hom (Γ, G) which we call layering and we show that the local rigidity holds if and only if Γ is finite.