Acylindrical hyperbolicity of groups acting on trees

Abstract

We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-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.

The published version of this paper contained a gap which is explained and partially fixed in the erratum arXiv:1711.09486. For the benefit of the readers, we have incorporated all necessary changes in this version

References in corpus (4)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Commensurating endomorphisms of acylindrically hyperbolic groups and applications
• Seifert Fibered Spaces: Notes for a course given in the Spring of 1993
• Bounded cohomology with coefficients in uniformly convex Banach spaces

Cited by in corpus (4)

• Transitivity degrees of countable groups and acylindrical hyperbolicity
• On purely loxodromic actions
• Orthogonal forms of Kac--Moody groups are acylindrically hyperbolic
• Finite extensions of $\mathcal{H}-$ and $\mathcal{A}\mathcal{H}-$accessible groups