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Acylindrical hyperbolicity of groups acting on trees. (English) Zbl 1360.20038

Math. Ann. 362, No. 3-4, 1055-1105 (2015); correction ibid. 373, No. 1-2, 895-900 (2019).
Summary: 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.

MSC:

20F67 Hyperbolic groups and nonpositively curved groups
20F65 Geometric group theory
20E08 Groups acting on trees
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
57M05 Fundamental group, presentations, free differential calculus
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