Actions of right-angled coxeter groups on the Croke-Kleiner space

Yulan Qing (Tufts)

Abstract: In this paper, we consider the geometry of actions of Right- angled Coxeter groups on a given CAT(0) space that is a universal cover of tori glued along closed curves. We require the action to be cocom- pact, properly discontinuous and by isometries and determine that the resulting gluing angle of the complex must be a right angle. We also prove that given the space we are studying, there is a unique Right-angled Coxeter group acting geometrically on that space. This study aims to contribute to the investigation of whether Right-angled Coxeter groups have unique boundaries.