
Journal of Lie Theory 26 (2016), No. 2, 371382 Copyright Heldermann Verlag 2016 Deformation of discontinuous groups acting on (H_{2n+1} × H_{2n+1}) / Δ Sami Dhieb Dept. of Mathematics, Faculty of Sciences of Sfax, Route de Soukra 3038, Sfax, Tunisia Sami.Dhieb@fss.rnu.tn [Abstractpdf] Let $H_{2n+1}$ be the $(2n+1)$dimensional Heisenberg group and $\Delta$ the diagonal subgroup of the product $P:=H_{2n+1}\times H_{2n+1}$. Given any discontinuous group $\Gamma$ for $P/\Delta$, we study some local geometric and topological features of the associated deformation space ${\cal T}(\Gamma,P;P/\Delta)$ such as rigidity, stability and Hausdorffness. In particular, we show that ${\cal T}(\Gamma,P;P/\Delta)$ is a Hausdorff space if and only if $\Gamma$ is a cocompact abelian discontinuous group for $P/\Delta$. Keywords: Heisenberg group, proper action, free action, rigidity, stability. MSC: 22E27; 32G05 [ Fulltextpdf (329 KB)] for subscribers only. 