9 citations · 16 across the 14 of their papers we have counts for
8 papers · 1 filter
Quasi-arithmetic hyperbolic Coxeter prisms
Nikolay Bogachev, Khusrav Yorov
In 1974, Kaplinskaja classified all simplicial straight hyperbolic Coxeter prisms. In this paper, we determine precisely which of these prisms are properly quasi-arithmetic or arit…
On quasi-arithmeticity of hyperbolic gluings
Nikolay Bogachev, Dmitry Guschin, Andrei Vesnin
We study a more general version of the gluings of hyperbolic orbifolds in the spirit of Gromov and Piatetski-Shapiro, where the gluing pieces, called the building blocks, are no lo…
Geometric and arithmetic properties of Löbell polyhedra
Nikolay Bogachev, Sami Douba
The Löbell polyhedra form an infinite family of compact right-angled hyperbolic polyhedra in dimension . We observe, through both elementary and more conceptual means, that the…
Kleinian sphere packings, reflection groups, and arithmeticity
Nikolay Bogachev, Alexander Kolpakov, Alex Kontorovich
In this paper we study crystallographic sphere packings and Kleinian sphere packings, introduced first by Kontorovich and Nakamura in 2017 and then studied further by Kapovich and…
On volumes of hyperbolic right-angled polyhedra
Stepan Alexandrov, Nikolay Bogachev, Andrei Egorov +1
In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space in three different cases: for ideal polyhedra with all vertices on…
Subspace stabilisers in hyperbolic lattices
Mikhail Belolipetsky, Nikolay Bogachev, Alexander Kolpakov +1
This paper shows that immersed totally geodesic -dimensional suborbifolds of -dimensional arithmetic hyperbolic orbifolds correspond to finite subgroups of the commensurator…
From geometry to arithmetic of compact hyperbolic Coxeter polytopes
Nikolay Bogachev
We establish some geometric constraints on compact Coxeter polytopes in hyperbolic spaces and show that these constraints can be a very useful tool for the classification problem o…
On faces of quasi-arithmetic Coxeter polytopes
Nikolay Bogachev, Alexander Kolpakov
We prove that each lower-dimensional face of a quasi-arithmetic Coxeter polytope, which happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a suffici…