Acylindrical accessibility for groups acting on ℝ-trees

Ilya Kapovich; Richard Weidmann

doi:10.1007/s00209-004-0731-3

Acylindrical accessibility for groups acting on ℝ-trees

Ilya Kapovich, Richard Weidmann

Mathematics

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Abstract

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

Original language	English (US)
Pages (from-to)	773-782
Number of pages	10
Journal	Mathematische Zeitschrift
Volume	249
Issue number	4
DOIs	https://doi.org/10.1007/s00209-004-0731-3
State	Published - Apr 2005

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General Mathematics

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10.1007/s00209-004-0731-3

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

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

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Acylindrical accessibility for groups acting on ℝ-trees

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