On boundaries of hyperbolic Coxeter groups

DOI10.1016/S0166-8641(99)00172-8zbMath0973.20030MaRDI QIDQ5928493

Alexander N. Dranishnikov

Publication date: 7 August 2001

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

boundaries of Coxeter groupsconvex geodesic spacesCoxeter systemsnerves of hyperbolic Coxeter groupssimplicial complexes

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Topological methods in group theory (57M07) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Hyperbolic groups and nonpositively curved groups (20F67) Other geometric groups, including crystallographic groups (20H15)

Related Items (6)

Hyperbolic Coxeter groups with Sierpiński carpet boundary ⋮ Hyperbolic right-angled Coxeter groups with boundaries as a Sierpiński carpet and a Menger curve ⋮ On equivariant homeomorphisms of boundaries of CAT(0) groups and Coxeter groups ⋮ Determination up to isomorphism of right-angled Coxeter systems. ⋮ Convex cocompactness in pseudo-Riemannian hyperbolic spaces ⋮ Boundaries of Coxeter groups and simplicial complexes with given links

Cites Work

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• Hyperbolization of polyhedra
• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Hyperbolic metric spaces and the exotic cohomology Novikov conjecture
• Boundaries of right-angled Coxeter groups with manifold nerves
• The cohomology of a Coxeter group with group ring coefficients
• Cell-like mappings and their generalizations
• On the virtual cohomological dimensions of Coxeter groups
• A proof of the generalized Schoenflies theorem
• Some applications of an approximation theorem for inverse limits
• Spaces of nonpositive curvature

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