Complete characterizations of hyperbolic Coxeter groups with Sierpiński curve boundary and with Menger curve boundary

Abstract

We give complete characterizations (in terms of nerves) of those word hyperbolic Coxeter groups whose Gromov boundary is homeomorphic to the Sierpiński curve and to the Menger curve, respectively. The justification is mostly an appropriate combination of various results from the literature.

Final accepted version

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• Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere