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 $\epsilon >0$ there is a finite subtree $Y_{\epsilon }\subseteq X$ of measure at most $2M(k-1)+\epsilon$ such that $G{Y}_{\epsilon }=X$. This generalizes theorems of Z.Sela and T.Delzant about actions on simplicial trees.

Final revised version, to appear in Math. Z