Actions of Right-Angled Coxeter Groups on the Croke Kleiner Spaces

2014/02/02 by Yulan Qing, Qing, Yulan
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1402.0154

Abstract

It is an open question whether right-angled Coxeter groups have unique group-equivariant visual boundaries. Croke and Kleiner present a right-angled Artin group with more than one visual boundary. In this paper we present a right-angled Coxeter group with non-unique equivariant visual boundary. The main theorem is that if right-angled Coxeter groups act geometrically on a Croke-Kleiner spaces, then the local angles in those spaces all have to be right angles. We present a specific right-angled Coxeter group with non-unique equivariant visual boundary. However, we conjecture that the right an- gled Coxeter groups that can act geometrically on a given CAT(0) space are far from unique.

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