Mathematische Annalen

, Volume 362, Issue 3–4, pp 1055–1105 | Cite as

Acylindrical hyperbolicity of groups acting on trees

  • Ashot MinasyanEmail author
  • Denis Osin


We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one-relator groups, automorphism groups of polynomial algebras, \(3\)-manifold groups and graph products. Acylindrical hyperbolicity is then used to obtain some results about the algebraic structure, analytic properties and measure equivalence rigidity of groups from these classes.

Mathematics Subject Classification

Primary 20F67 20F65 20E08 Secondary 20E34 20E06 57M05 



The authors would like to thank Henry Wilton for helpful discussions of \(3\)-manifolds. We are also grateful to Jack Button for his valuable comments, and to Stephane Lamy for pointing out an error in an earlier version of the paper. Finally, we would like to thank the referee for a careful reading of this article.


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Authors and Affiliations

  1. 1.Mathematical SciencesUniversity of Southampton, HighfieldSouthamptonUK
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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