Deformation of discontinuous groups acting on (H2n+1 × H2n+1) / Δ
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 371-382
Voir la notice de l'article provenant de la source Heldermann Verlag
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 $P/\Delta$.
Classification :
22E27, 32G05
Mots-clés : Heisenberg group, proper action, free action, rigidity, stability
Mots-clés : Heisenberg group, proper action, free action, rigidity, stability
Affiliations des auteurs :
Sami Dhieb 1
Sami Dhieb. Deformation of discontinuous groups acting on (H2n+1 × H2n+1) / Δ. Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 371-382. http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a2/
@article{JOLT_2016_26_2_a2,
author = {Sami Dhieb},
title = {Deformation of discontinuous groups acting on {(H\protect\textsubscript{2n+1}} {\texttimes} {H\protect\textsubscript{2n+1})} / {\ensuremath{\Delta}}},
journal = {Journal of Lie Theory},
pages = {371--382},
year = {2016},
volume = {26},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a2/}
}