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Characterizing divergence in right-angled Coxeter groups

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Ivan Levcovitz (Technion)

A main goal in geometric group theory is to understand finitely generated groups up to quasi-isometry (a coarse geometric equivalence relation on Cayley graphs). Right-angled Coxeter groups (RACGs) are a well-studied, wide class of groups whose coarse geometry is not well understood. One of the few available quasi-isometry invariants known to distinguish non-relatively hyperbolic RACGs is the divergence function, which roughly measures the maximum rate at which a pair of geodesic rays in a Cayley graph can diverge from one another. In this talk I will discuss a recent result that completely classifies divergence functions in RACGs, gives a simple method of computing them and links divergence to other known quasi-isometry invariants.