Abstract
We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A Γ with connected defining graph. We use this to prove that the divergence of A Γ 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 A Γ. We also show that every non-abelian subgroup of A Γ has an infinite-dimensional space of non-trivial quasimorphisms.
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R. Charney was partially supported by NSF grant DMS 0705396.
J. Behrstock was partially supported by NSF grant DMS 0812513 and the Sloan Foundation.
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Behrstock, J., Charney, R. Divergence and quasimorphisms of right-angled Artin groups. Math. Ann. 352, 339–356 (2012). https://doi.org/10.1007/s00208-011-0641-8
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DOI: https://doi.org/10.1007/s00208-011-0641-8