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Abstract Let ( W , S ) be a hyperbolic right-angled Coxeter system whose nerve is a 1-dimensional strongly co-connected simplicial complex, where “strongly co-connected” is defined in this paper.… Click to show full abstract
Abstract Let ( W , S ) be a hyperbolic right-angled Coxeter system whose nerve is a 1-dimensional strongly co-connected simplicial complex, where “strongly co-connected” is defined in this paper. Then we provide characterizations of the Coxeter group W whose boundary ∂W is a Sierpinski carpet and a Menger curve. Using this result, we construct hyperbolic right-angled Coxeter groups with boundaries as their universal curves. We note that hyperbolic non-right-angled Coxeter groups with boundaries as their universal curves have been constructed in N. Benakli's PhD Thesis [3] .
Journal Title: Topology and its Applications
Year Published: 2019
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