On Faces of Quasi-arithmetic Coxeter Polytopes-Reference-Cited by-同舟云学术

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On Faces of Quasi-arithmetic Coxeter Polytopes

Published:2021-01-19 Issue:4 Volume:2021 Page:3078-3096
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bogachev Nikolay¹²³,Kolpakov Alexander²⁴

Affiliation:

1. Skolkovo Institute of Science and Technology, 143026 Skolkovo, Russia

2. Laboratory of Combinatorial and Geometric Structures, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia

3. Caucasus Mathematical Centre, Adyghe State University, 385000 Maikop, Russia

4. Institut de Mathématiques, Université de Neuchâtel, 2000 Neuchâtel, Switzerland

Abstract

Abstract 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 condition for a codimension $1$ face to be actually arithmetic, as well as a few computed examples. In memoriam È. B. Vinberg 1937–2020

Funder

Swiss National Science Foundation

Russian Science Foundation

Russian Federation Government

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/4/3078/36271451/rnaa278.pdf

Reference37 articles.

1. Finiteness of Arithmetic Kleinian Reflection Groups;Agol,2006

2. Finiteness of arithmetic hyperbolic reflection groups;Agol;Groups Geom. Dyn.,2008

3. Infinitely many hyperbolic Coxeter groups through dimension 19;Allcock;Geom. Topol.,2006

4. Systoles of hyperbolic manifolds;Belolipetsky;Algebraic Geom. Topol.,2011

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1. Infinitely many commensurability classes of compact Coxeter polyhedra in H4 and H5;Advances in Mathematics;2024-06

2. Kleinian sphere packings, reflection groups, and arithmeticity;Mathematics of Computation;2023-07-26

3. Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes;Transactions of the American Mathematical Society;2023-07-20

4. FROM GEOMETRY TO ARITHMETIC OF COMPACT HYPERBOLIC COXETER POLYTOPES;Transformation Groups;2022-06-03

5. Infinitely many quasi-arithmetic maximal reflection groups;P AM MATH SOC;2022-01-16

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