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Acylindrical accessibility for groups acting on $$\mathbb{R}$$-trees. (English) Zbl 1080.20035
Summary: We prove an acylindrical accessibility theorem for finitely generated groups acting on $$\mathbb{R}$$-trees. Namely, we show that if $$G$$ is a freely indecomposable non-cyclic $$k$$-generated group acting minimally and $$D$$-acylindrically on an $$\mathbb{R}$$-tree $$X$$ then there is a finite subtree $$T_\varepsilon\subseteq X$$ of measure at most $$2D(k-1)+\varepsilon$$ such that $$GT_\varepsilon=X$$. This generalizes theorems of Z. Sela and T. Delzant about actions on simplicial trees.

##### MSC:
 20F67 Hyperbolic groups and nonpositively curved groups 20E08 Groups acting on trees
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##### References:
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