Notes on right-angled Coxeter polyhedra in hyperbolic spaces

被引：12

作者：

Dufour, Guillaume ^{[1
]}

机构：

[1] Univ Paris 11, Dept Math, F-91405 Orsay, France

来源：

GEOMETRIAE DEDICATA | 2010年 / 147卷 / 01期

关键词：

Hyperbolic geometry; Combinatorics; Right-angled Coxeter polyhedra;

D O I：

10.1007/s10711-009-9454-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that (finite volume) right-angled Coxeter polyhedra may exist in hyperbolic spaces only in dimension at most 12. This is a slight improvement on a theorem of Potyagailo and Vinberg stated in Potyagailo and Vinberg (Comment Math Helv 80:1-12, 2005).

引用

页码：277 / 282

页数：6

共 50 条

[31] Boundaries of right-angled hyperbolic buildings
Dymara, Jan
Osajda, Damian
[J]. FUNDAMENTA MATHEMATICAE, 2007, 197 : 123 - 165
[32] On right-angled polygons in hyperbolic space
Edoardo Dotti
Simon T. Drewitz
[J]. Geometriae Dedicata, 2019, 200 : 45 - 59
[33] Commensurability classification of a family of right-angled coxeter groups
Crisp, John
Paoluzzi, Luisa
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (07) : 2343 - 2349
[34] Characterizing divergence and thickness in right-angled Coxeter groups
Levcovitz, Ivan
[J]. JOURNAL OF TOPOLOGY, 2022, 15 (04) : 2143 - 2173
[35] PROPER AFFINE ACTIONS FOR RIGHT-ANGLED COXETER GROUPS
Danciger, Jeffrey
Gueritaud, Francois
Kassel, Fanny
[J]. DUKE MATHEMATICAL JOURNAL, 2020, 169 (12) : 2231 - 2280
[36] The Associated Lie Algebra of a Right-Angled Coxeter Group
Veryovkin, Ya. A.
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2019, 305 (01) : 53 - 62
[37] On right-angled polygons in hyperbolic space
Dotti, Edoardo
Drewitz, Simon T.
[J]. GEOMETRIAE DEDICATA, 2019, 200 (01) : 45 - 59
[38] Right-angled Coxeter groups with Menger curve boundary
Danielski, Daniel
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2022, 54 (03) : 977 - 995
[39] Local connectivity of right-angled Coxeter group boundaries
Mihalik, Michael
Ruane, Kim
Tschantz, Steve
[J]. JOURNAL OF GROUP THEORY, 2007, 10 (04) : 531 - 560
[40] Boundaries of right-angled Coxeter groups with manifold nerves
Fischer, H
[J]. TOPOLOGY, 2003, 42 (02) : 423 - 446

← 1 2 3 4 5 →