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 …
On superintegral Kleinian sphere packings, bugs, and arithmetic groups
M Kapovich, A Kontorovich - Journal für die reine und angewandte …, 2023 - degruyter.com
We develop the notion of a Kleinian Sphere Packing, a generalization of “crystallographic”(
Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura, Geometry …
Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura, Geometry …
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 …
Real reflections, commutators, and cross-ratios in complex hyperbolic space
J Paupert, P Will - Groups, Geometry, and Dynamics, 2017 - ems.press
Real reflections, commutators, and cross-ratios in complex hyperbolic space Page 1 Groups
Geom. Dyn. 11 (2017), 311–352 DOI 10.4171/GGD/398 Groups, Geometry, and Dynamics © …
Geom. Dyn. 11 (2017), 311–352 DOI 10.4171/GGD/398 Groups, Geometry, and Dynamics © …
A taxonomy of crystallographic sphere packings
D Chait-Roth, A Cui, Z Stier - Journal of Number Theory, 2020 - Elsevier
This paper seeks to catalogue and examine crystallographic sphere packings as defined by
Kontorovich and Nakamura. There exist at least three sources which give rise to …
Kontorovich and Nakamura. There exist at least three sources which give rise to …
Geometry and arithmetic of crystallographic sphere packings
A Kontorovich, K Nakamura - arxiv preprint arxiv:1712.00147, 2017 - arxiv.org
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 …
Picard modular groups generated by complex reflections
A Mark, J Paupert, D Polletta - arxiv preprint arxiv:2112.07797, 2021 - arxiv.org
In this short note we use the presentations found in\cite {MP} and\cite {Po} to show that the
Picard modular groups ${\rm PU}(2, 1,\mathcal {O} _d) $ with $ d= 1, 3, 7$(respectively the …
Picard modular groups ${\rm PU}(2, 1,\mathcal {O} _d) $ with $ d= 1, 3, 7$(respectively the …
Dirichlet-Ford domains and Double Dirichlet domains
E Jespers, SO Juriaans, A Kiefer… - Bulletin of the Belgian …, 2016 - projecteuclid.org
We continue investigations started by Lakeland on Fuchsian and Kleinian groups which
have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space …
have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space …
A Taxonomy of Crystallographic Sphere Packings
D Chait, A Cui, Z Stier - arxiv preprint arxiv:1903.03563, 2019 - arxiv.org
The Apollonian circle packing, generated from three mutually-tangent circles in the plane,
has inspired over the past half-century the study of other classes of space-filling packings …
has inspired over the past half-century the study of other classes of space-filling packings …
[PDF][PDF] Hyperbolic Geometry and Algebraic geometry, Seoul-Austin, 2014/15
I Dolgachev - 2015 - Citeseer
This is an extending version of my lectures in Seoul in October 2014 and in Austin in
February 2015. The main topic covered in the lectures is an interrelationship between the …
February 2015. The main topic covered in the lectures is an interrelationship between the …