Locally rigid right-angled Coxeter groups with Fuchsian ends in dimension 5

TL;DR

This paper constructs a specific 5-dimensional right-angled polytope whose associated Coxeter groups with Fuchsian ends are proven to be locally rigid, advancing understanding of geometric structures in higher dimensions.

Contribution

It introduces a new 5-polytope with finite volume that ensures local rigidity for all related Coxeter groups with Fuchsian ends.

Findings

All Coxeter groups with Fuchsian ends from the polytope are locally rigid.

The construction provides new examples of rigid geometric structures in dimension 5.

Advances the study of Coxeter groups and hyperbolic geometry in higher dimensions.

Abstract

In this paper, we construct a right-angled 5-polytope P of finite volume such that all the right-angled Coxeter groups with Fuchsian ends obtained from P are locally rigid.