Infinitely many hyperbolic Coxeter groups through dimension 19.

DOI10.2140/gt.2006.10.737zbMath1133.20025arXiv0903.0138OpenAlexW3104406869WikidataQ54259369 ScholiaQ54259369MaRDI QIDQ2501697

Daniel Allcock

Publication date: 11 September 2006

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.0138

zbMATH Keywords

Leech latticecocompact Coxeter groupsCoxeter polyhedrafinite-covolume Coxeter groups

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Discrete subgroups of Lie groups (22E40)

Related Items (15)

Finiteness of maximal geodesic submanifolds in hyperbolic hybrids ⋮ Even more infinite ball packings from Lorentzian root systems ⋮ Kleinian sphere packings, reflection groups, and arithmeticity ⋮ Lannér diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes ⋮ Finiteness theorems for congruence reflection groups. ⋮ From geometry to arithmetic of compact hyperbolic Coxeter polytopes ⋮ Compact hyperbolic Coxeter four-dimensional polytopes with eight facets ⋮ On hyperbolic Coxeter polytopes with mutually intersecting facets ⋮ On $d$-dimensional compact hyperbolic Coxeter polytopes with $d+4$ facets ⋮ Essential hyperbolic Coxeter polytopes ⋮ Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle ⋮ Arithmetic hyperbolic reflection groups ⋮ Coxeter polytopes with a unique pair of non-intersecting facets ⋮ Local rigidity in quaternionic hyperbolic space ⋮ Root systems for Lorentzian Kac–Moody algebras in rank 3

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The two most algebraic K3 surfaces
• Compact hyperbolic Coxeter \(n\)-polytopes with \(n+3\) facets
• Groups of automorphisms of unimodular hyperbolic quadratic forms over the ring \({\mathbb{Z}}[(\sqrt{5}+1)/2\)]
• Automorphism groups of Lorentzian lattices
• On right-angled reflection groups in hyperbolic spaces.
• Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces
• Hyperbolic Coxeter \(n\)-polytopes with \(n+2\) facets
• The classification of compact hyperbolic Coxeter \(d\)-polytopes with \(d+2\) facets
• Hyperbolic Coxeter $n$-polytopes with $n+3$ facets
• Leech roots and Vinberg groups
• ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS

This page was built for publication: Infinitely many hyperbolic Coxeter groups through dimension 19.