Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers.

DOI10.2140/agt.2013.13.1001zbMath1281.20044OpenAlexW2077032502MaRDI QIDQ1948306

Ruth Kellerhals

Publication date: 3 May 2013

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

Full work available at URL: https://doi.org/10.2140/agt.2013.13.1001

zbMATH Keywords

growth ratesPisot numbershyperbolic Coxeter groupscuspshyperbolic 3-orbifolds

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Discrete subgroups of Lie groups (22E40) Hyperbolic groups and nonpositively curved groups (20F67) Reflection groups, reflection geometries (51F15)

Related Items (7)

Hyperbolic Coxeter groups of minimal growth rates in higher dimensions ⋮ Exponential growth rates of free and amalgamated products. ⋮ Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups ⋮ The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space ⋮ Seventy years of Salem numbers ⋮ Hyperbolic Coxeter groups and minimal growth rates in dimensions four and five ⋮ On the growth rate of ideal Coxeter groups in hyperbolic 3-space.

Cites Work

• On the growth of hyperbolic 3-dimensional generalized simplex reflection groups.
• Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers
• On the growth of cocompact hyperbolic Coxeter groups.
• The growth function of Coxeter garlands in \(\mathbb H^4\).
• Reciprocity of growth functions of Coxeter groups
• Growth of planar Coxeter groups, P.V.numbers and Salem numbers
• Groupes de Coxeter infinis non affines. (Infinite non affine Coxeter groups)
• Growth series of Coxeter groups and Salem numbers
• Galois theory.
• Discrete groups generated by reflections
• Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces
• The size of hyperbolic Coxeter simplex
• The orders of the finite Chevalley groups
• Hyperbolic reflection groups
• The cusped hyperbolic 3-orbifold of minimum volume
• The Lehmer Polynomial and Pretzel Links
• The Minimal Growth Rate of Cocompact Coxeter Groups in Hyperbolic 3-space
• Endomorphisms of linear algebraic groups
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer
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