Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces

Abstract

We consider a cocompact discrete reflection group $W$ of a CAT(0) space $X$. Then $W$ becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex $\Sigma (W,S)$ and the CAT(0) space $X$, and show several analogous results about the limit set of a parabolic subgroup of the Coxeter group $W$.

Cited by in corpus (1)

• On equivariant homeomorphisms of boundaries of CAT(0) groups