9 citations · 16 across the 14 of their papers we have counts for
16 papers
Singularity of harmonic measures for hyperbolic lattices
Nikolay Bogachev
Let , , be a cocompact lattice containing a convex cocompact codimension-one subgroup in the sense of Sageev. We prove that every finitely sup…
Proof of the positive trace gap conjecture
Nikolay Bogachev
We prove that a lattice in or has positive trace gap, meaning that its traces are uniformly separated, if and only if i…
Random walks on cocompact Fuchsian and Kleinian groups
Nikolay Bogachev, Peter Kosenko, Giulio Tiozzo
The question of the singularity at infinity of the hitting measure of random walks has a long history, originating from the work of Furstenberg in the 1960s. In 2011, Kaimanovich a…
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…
Arithmetic trialitarian hyperbolic lattices are not LERF
Nikolay Bogachev, Leone Slavich, Hongbin Sun
A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1…
Infinitely many commensurability classes of compact Coxeter polyhedra in and
Nikolay Bogachev, Sami Douba, Jean Raimbault
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…
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…
Thin hyperbolic reflection groups
Nikolay Bogachev, Alexander Kolpakov
We study a family of Zariski dense finitely generated discrete subgroups of , , defined by the following property: any group in this fam…
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…
Classification of -reflective anisotropic hyperbolic lattices of rank
Nikolay V. Bogachev
A hyperbolic lattice is called \textit{-reflective} if its automorphism group is generated by - and -reflections up to finite index. In this paper we prove that the…
Reflective anisotropic hyperbolic lattices of rank
Nikolay V. Bogachev
A hyperbolic lattice is called \textit{-reflective} if the subgroup of its automorphism group generated by all - and -reflections is of finite index. The main result of…