Right-angled Coxeter groups with n-dimensional Sierpi\'nski compacta as boundaries

Jacek Świątkowski

doi:10.1112/topo.12026

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arXiv · 1603.02152

Right-angled Coxeter groups with n-dimensional Sierpi\'nski compacta as boundaries

Jacek Świątkowski

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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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BibTeX RIS

Jacek Świątkowski. 2016-03-07. Right-angled Coxeter groups with n-dimensional Sierpi\'nski compacta as boundaries. https://doi.org/10.1112/topo.12026

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