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arXiv · 2608.07350

Profinite rigidity in lattices of $\mathrm{PSL}(2,\mathbb{C})$

Xiaoyu Xu
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Abstract

A finitely generated group is profinitely rigid among a class of finitely generated groups if it can be distinguished among this class by its set of finite quotient groups. This paper proves that all lattices in $\mathrm{PSL}(2,\mathbb{C})$ are profinitely rigid among themselves. In addition, for any lattice $Γ\le \mathrm{PSL}(2,\mathbb{C})$, it is proven that $\mathrm{Out}(\widehatΓ)\cong \mathrm{Out}(Γ)$, where $\widehatΓ$ denotes the profinite completion of $Γ$.

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Xiaoyu Xu. 2026-08-07. Profinite rigidity in lattices of $\mathrm{PSL}(2,\mathbb{C})$. https://arxiv.org/abs/2608.07350

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