Geometry of right-angled Coxeter groups on the Croke-Kleiner spaces

Abstract

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with $\pi /2$ angles between reflecting axes, while the quasi-isometric right-angled Artin group can act with angles that are any real number in the range $(0,\pi /2]$. The contrast between the two examples shows that in this case a right-angled Coxeter group is geometrically more "rigid" than its quasi isometric counterpart.

10 pages, published. arXiv admin note: substantial text overlap with arXiv:1402.0154