Guirardel, Vincent Approximations of stable actions on \(\mathbb{R}\)-trees. (English) Zbl 0979.20026 Comment. Math. Helv. 73, No. 1, 89-121 (1998). 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. Cited in 22 Documents 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 Keywords:stable actions on trees; finitely presented groups; hyperbolic groups; simplicial trees PDFBibTeX XMLCite \textit{V. Guirardel}, Comment. Math. Helv. 73, No. 1, 89--121 (1998; Zbl 0979.20026) Full Text: DOI