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arXiv · 2608.27274

On some aspects of discrete groups acting ergodically on the boundary

Subhadip Dey·Mikołaj Frączyk·Sebastian Hurtado
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Abstract

We show that if $G$ is a real semisimple Lie group and $\Gamma 2$. The examples arise from lattices $\Gamma<H= SO(n,1)$ and their deformations in $G$. Perhaps more importantly, we describe a new approach to studying deformations of such lattices by relating them to deformations of the smooth right-translation action of $SO(n-1,1)$ on $\Gamma\backslash H$. This correspondence allows us to apply recent results of DeWitt and Dolgopyat on smooth group actions and to give examples where the right-translation action of $SO(n-1,1)$ on $\Gamma\backslash H$ can fail to be $C^0$-locally rigid.

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Subhadip Dey, Mikołaj Frączyk, Sebastian Hurtado. 2026-08-27. On some aspects of discrete groups acting ergodically on the boundary. https://arxiv.org/abs/2608.27274

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