Divergence and Quasimorphisms of Right-angled Artin Groups

We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group AΓ with connected defining graph. We use this to prove that the divergence of AΓ is linear if Γ is a join and quadratic otherwise. As an application, we give a complete description of the cut points in any asymptotic cone of AΓ. We also show that every non-abelian subgroup of AΓ has an infinite-dimensional space of non-trivial quasimorphisms.