Journal of Lie Theory

no. 2
Deformation of discontinuous groups acting on (H2n+1 × H2n+1) / Δ
Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 371-382
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 $P/\Delta$.
DOI: 10.5802/jolt.895
Classification: 22E27, 32G05
Keywords: Heisenberg group, proper action, free action, rigidity, stability 
@article{JOLT_2016_26_2_a2,
     author = {S. 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},
     doi = {10.5802/jolt.895},
     zbl = {1344.22001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.895/}
}
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%A S. Dhieb
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S. Dhieb. Deformation  of discontinuous groups acting on (H2n+1 × H2n+1) / Δ. Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 371-382. doi: 10.5802/jolt.895

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