Acylindrical hyperbolicity for groups acting on complexes with large links

Alexandre Martin

Published 2015-12-23Version 1

We give a criterion for acylindrical hyperbolicity in the case of groups acting on polyhedral complexes with some vertices having unbounded links, generalising a criterion of Minasyan--Osin for actions on simplicial trees. As an application, we prove that the subgroup $\mbox{Tame}(\mbox{SL}_2)$ of the $3$-dimensional Cremona group $\mbox{Bir}(\mathbb{P}^3(\mathbb{C}))$ is acylindrically hyperbolic.