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

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

2002-10-19

arxiv.org/abs/math/0210308v2

Mathematics

Group Theory

Final revised version, to appear in Math. Z

Scientific paper

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 $GY_{\epsilon}=X$. This generalizes theorems of Z.Sela and T.Delzant about actions on simplicial trees.

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