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Divergence and quasimorphisms of right-angled Artin groups

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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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Authors and Affiliations

  1. Department of Mathematics, Lehman College, CUNY Bronx, NY, 10468, USA

    Jason Behrstock

  2. Department of Mathematics, Brandeis University, Waltham, MA, 02453, USA

    Ruth Charney

Authors
  1. Jason Behrstock
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  2. Ruth Charney
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Corresponding author

Correspondence to Ruth Charney.

Additional information

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

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