Locally Rigid Right-angled Coxeter Groups with Fuchsian Ends in Dimension 5

Abstract

In this paper, we construct a right-angled $5$-polytope $\mathcal{P}$ of finite volume such that all the right-angled Coxeter groups with Fuchsian ends obtained from $\mathcal{P}$ are locally rigid. This is the first explicit example of locally rigid discrete subgroups of $\text{Isom}\left({\mathrm{ℍ}}^5\right)$ with Fuchsian ends.