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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.

MSC:
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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