Infinitely many commensurability classes of compact Coxeter polyhedra in H 4 and H 5

Infinitude des classes de commensurabilités de groupes de Coxeter dans les espaces hyperboliques de dimension 4 et 5

Nikolay Bogachev (1) , Sami Douba (2) , Jean Raimbault (3)

1 University of Toronto
2 IHES - Institut des Hautes Études Scientifiques
3 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Mathématiques [math]

Nikolay Bogachev, Sami Douba, Jean Raimbault. Infinitely many commensurability classes of compact Coxeter polyhedra in H 4 and H 5. Advances in Mathematics, 2024, 448, pp.109705. ⟨10.1016/j.aim.2024.109705⟩. ⟨hal-04625560⟩