Notes on thin matrix groups
P Sarnak - Thin groups and superstrong approximation, 2014 - books.google.com
We give a brief overview of the developments in the theory, especially the fundamental
expansion theorem. Applications to diophantine problems on orbits of integer matrix groups …
expansion theorem. Applications to diophantine problems on orbits of integer matrix groups …
Arithmetic hyperbolic reflection groups
M Belolipetsky - Bulletin of the American Mathematical Society, 2016 - ams.org
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $
n $-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of …
n $-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of …
Infinitely many commensurability classes of compact Coxeter polyhedra in H4 and H5
N Bogachev, S Douba, J Raimbault - Advances in Mathematics, 2024 - Elsevier
Infinitely many commensurability classes of compact Coxeter polyhedra in H4 and H5 -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
Geometry and arithmetic of crystallographic sphere packings
A Kontorovich, K Nakamura - Proceedings of the National …, 2019 - National Acad Sciences
We introduce the notion of a “crystallographic sphere packing,” defined to be one whose
limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension …
limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension …
Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds
The Riley slice is arguably the simplest example of a moduli space of Kleinian groups; it is
naturally embedded in $\mathbb {C} $, and has a natural coordinate system (introduced by …
naturally embedded in $\mathbb {C} $, and has a natural coordinate system (introduced by …
On volumes of arithmetic quotients of PO (n, 1)°, n odd
M Belolipetsky, V Emery - Proceedings of the London …, 2012 - academic.oup.com
We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional
orbifolds (compact and non-compact), for every odd dimension n≥ 5. Combined with the …
orbifolds (compact and non-compact), for every odd dimension n≥ 5. Combined with the …
On faces of quasi-arithmetic Coxeter polytopes
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 sufficient …
happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a sufficient …
A new proof of finiteness of maximal arithmetic reflection groups
We give a new proof of the finiteness of maximal arithmetic reflection groups. Our proof is
novel in that it makes no use of trace formulas or other tools from the theory of automorphic …
novel in that it makes no use of trace formulas or other tools from the theory of automorphic …
Geometric and arithmetic properties of L\" obell polyhedra
N Bogachev, S Douba - arxiv preprint arxiv:2304.12590, 2023 - arxiv.org
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 …
in dimension $3 $. We observe, through both elementary and more conceptual means, that …
Coxeter polytopes and Benjamini--Schramm convergence
J Raimbault - arxiv preprint arxiv:2209.03002, 2022 - arxiv.org
We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular
neighbourhood of its boundary, and use this to give a new proof for the finiteness of …
neighbourhood of its boundary, and use this to give a new proof for the finiteness of …