Acylindrical accessibility for groups acting on $\mathbf R$-trees

Abstract

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an $\mathbf R$-tree $X$ then for any $ε>0$ there is a finite subtree $Y_ε\subseteq X$ of measure at most $2M(k-1)+ε$ such that $GY_ε=X$. This generalizes theorems of Z.Sela and T.Delzant about actions on simplicial trees.