Right-angled Coxeter groups with n-dimensional Sierpiński compacta as boundaries

Abstract

For arbitrary integer n, we describe a large class of right-angled Coxeter systems for which the visual baundary (of the corresponding Coxeter-Davis complex) is homeomorphic to the n-dimensional Sierpiński compactum. We also provide a necessary and sufficient condition for a planar simplicial complex L under which the right-angled Coxeter system whose nerve is L has the visual boundary homeomorphic to the Sierpiński curve.

25 pages, 1 figure

References in corpus (3)

• On asymptotically hereditarily aspherical groups
• Trees of manifolds as boundaries of spaces and groups
• Hyperbolic Coxeter groups with Sierpiński carpet boundary

Cited by in corpus (1)

• Trees of metric compacta and trees of manifolds