Reflection subgroups of Coxeter groups

DOI10.1090/S0002-9947-09-04859-4zbMath1198.20035arXiv0705.0426MaRDI QIDQ5189153

Pavel Tumarkin, A. A. Felikson

Publication date: 8 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.0426

zbMATH Keywords

Coxeter groupsEuclidean complexesfinite index reflection subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Reflection groups, reflection geometries (51F15)

Related Items (8)

On some convex cocompact groups in real hyperbolic space. ⋮ Coxeter groups and meridional rank of links ⋮ Infinitely many quasi-arithmetic maximal reflection groups ⋮ Hyperbolic subalgebras of hyperbolic Kac-Moody algebras ⋮ Reflection subgroups of odd-angled Coxeter groups. ⋮ Essential hyperbolic Coxeter polytopes ⋮ Coxeter groups, quiver mutations and geometric manifolds ⋮ Representations of polygons of finite groups.

Cites Work

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• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Reflection subgroups of Coxeter systems
• Coxeter decompositions of hyperbolic polygons
• Two-generator discrete subgroups of \(\text{Isom}(\mathbb{H}^2)\) containing orientation-reversing elements
• Reflection subgroups of reflection groups.
• Intersection of plane boundaries of a polytope with acute angles
• Some remarks on involutions in coxeter groups

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