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Approximations of stable actions on \(\mathbb{R}\)-trees. (English) Zbl 0979.20026
Summary: This article shows how to approximate a stable action of a finitely presented group on an \(\mathbb{R}\)-tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an \(\mathbb{R}\)-tree can be approximated by a small action of the same group on a simplicial tree. The techniques we use highly rely on Rips’s study of stable actions on \(\mathbb{R}\)-trees and on the dynamical study of exotic components by D. Gaboriau.

20E08 Groups acting on trees
20F65 Geometric group theory
57M07 Topological methods in group theory
20F67 Hyperbolic groups and nonpositively curved groups
05C05 Trees
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