Hyperbolic right-angled Coxeter groups with boundaries as a Sierpinski carpet and a Menger curve

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 partial derivative 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]. (C) 2019 Elsevier B.V. All rights reserved.