Minimality of the boundary of a right-angled Coxeter system

DOI10.1090/S0002-9939-08-09585-3zbMath1226.20035arXivmath/0606020OpenAlexW2025764061MaRDI QIDQ3617577

Tetsuya Hosaka

Publication date: 30 March 2009

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

Full work available at URL: https://arxiv.org/abs/math/0606020

zbMATH Keywords

parabolic subgroupsboundaries of Coxeter groupsCoxeter systemsgeometric actionsDavis complexesactions of right-angled Coxeter groups

Mathematics Subject Classification ID

Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Topological methods in group theory (57M07)

Related Items

CAT(0) groups and Coxeter groups whose boundaries are scrambled sets.

Cites Work

• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Determination up to isomorphism of right-angled Coxeter systems.
• Parabolic subgroups of finite index in Coxeter groups.
• A cut point theorem for CAT(0) groups.
• Superrigidity for irreducible lattices and geometric splitting
• A splitting theorem for \(\text{CAT}(0)\) spaces with the geodesic extension property.
• The cohomology of a Coxeter group with group ring coefficients
• On dense orbits in the boundary of a Coxeter system
• Dense subsets of the boundary of a Coxeter system
• Fixed points in boundaries of negatively curved groups
• Boundaries of nonpositively curved groups of the form G × ℤⁿ
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