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

Ilya Kapovich·Richard Weidmann
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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.

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Ilya Kapovich, Richard Weidmann. 2004-08-27. Acylindrical accessibility for groups acting on $\mathbf R$-trees. https://arxiv.org/abs/math/0210308

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