Divergence of CAT(0) Cube Complexes and Right-Angled Coxeter Groups

Ivan Levcovitz (CUNY)

Abstract: The divergence function of a metric space, a quasi-isometry invariant, roughly measures the rate which pairs of geodesic rays stray apart. We will present new results regarding divergence functions of CAT(0) cube complexes. Right-angled Coxeter groups, in particular, exhibit a rich spectrum of possible divergence functions. The talk will give special focus to applications of our results to these groups. Applications to the theory of random right-angled Coxeter groups will also be briefly discussed.