Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Bogachev, Nikolay"'
Autor:
Bogachev, Nikolay, Yorov, Khusrav
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 arithmetic. We also present some observations regarding commensurability c
Externí odkaz:
http://arxiv.org/abs/2312.17193
A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work
Externí odkaz:
http://arxiv.org/abs/2310.20611
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.
Comment: Final version, t
Comment: Final version, t
Externí odkaz:
http://arxiv.org/abs/2309.07691
We study a more general version of the hybrid construction of Gromov and Piatetski--Shapiro, where the building blocks are no longer assumed to be arithmetic. We show that if such a general hyberbolic hybrid of dimension $\geqslant 3$ is quasi-arithm
Externí odkaz:
http://arxiv.org/abs/2307.07000
Autor:
Bogachev, Nikolay, Douba, Sami
The L\"obell polyhedra form an infinite family of compact right-angled hyperbolic polyhedra in dimension $3$. We observe, through both elementary and more conceptual means, that the ``systoles'' of the L\"obell polyhedra approach $0$, so that these p
Externí odkaz:
http://arxiv.org/abs/2304.12590
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 Kontorovich in 2021. In particular, we solve the problem of existence
Externí odkaz:
http://arxiv.org/abs/2203.01973
Autor:
Bogachev, Nikolay, Kolpakov, Alexander
We study a family of Zariski dense finitely generated discrete subgroups of $\mathrm{Isom}(\mathbb{H}^d)$, $d \geqslant 2$, defined by the following property: any group in this family contains at least one reflection in a hyperplane. As an applicatio
Externí odkaz:
http://arxiv.org/abs/2112.14642
In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite
Externí odkaz:
http://arxiv.org/abs/2111.08789
Publikováno v:
In Advances in Mathematics June 2024 448
This paper shows that immersed totally geodesic $m$-dimensional suborbifolds of $n$-dimensional arithmetic hyperbolic orbifolds correspond to finite subgroups of the commensurator whenever $m \geqslant \lfloor \frac{n}{2} \rfloor$. We call such total
Externí odkaz:
http://arxiv.org/abs/2105.06897