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

摘要

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