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Journal of Lie Theory 26 (2016), No. 2, 371--382
Copyright Heldermann Verlag 2016

Deformation of discontinuous groups acting on (H2n+1 × H2n+1) / Δ

Sami Dhieb
Dept. of Mathematics, Faculty of Sciences of Sfax, Route de Soukra 3038, Sfax, Tunisia


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

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