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Right-angled Coxeter groups with n-dimensional Sierpiński compacta as boundaries (1603.02152v1)
Published 7 Mar 2016 in math.GT
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 Sierpi\'nski 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 Sierpi\'nski curve.
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