Infinitely many commensurability classes of compact Coxeter polyhedra in $\mathbb{H}^4$ and $\mathbb{H}^5$

Nikolay Bogachev; Sami Douba; Jean Raimbault

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arXiv · 2309.07691

Infinitely many commensurability classes of compact Coxeter polyhedra in $\mathbb{H}^4$ and $\mathbb{H}^5$

Nikolay Bogachev·Sami Douba·Jean Raimbault

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Abstract

We prove that certain families of compact Coxeter polyhedra in 4- and 5-dimensional hyperbolic space constructed by Makarov give rise to infinitely many commensurability classes of reflection groups in these dimensions.

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Nikolay Bogachev, Sami Douba, Jean Raimbault. 2023-09-14. Infinitely many commensurability classes of compact Coxeter polyhedra in $\mathbb{H}^4$ and $\mathbb{H}^5$. https://arxiv.org/abs/2309.07691

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