Divergence in right-angled Coxeter groups

Abstract

The divergence of a pair of geodesics emanating from a point in a metric space is a measure of how quickly they are moving away from each other. In Euclidean space divergence is linear, while in hyperbolic space divergence is exponential. Gersten used this idea to define a quasi-isometry invariant for groups, which has been investigated for classes of groups including 3-manifold groups, mapping class groups and right-angled Artin groups. I will discuss joint work with Pallavi Dani on divergence in the class of right-angled Coxeter groups.