This article shows how to approximate a stable action of a finitely presented group on an -tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an -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 -trees and on the dynamical study of exotic components by D. Gaboriau.
Cite this article
Vincent Guirardel, Approximations of stable actions on -trees. Comment. Math. Helv. 73 (1998), no. 1, pp. 89–121DOI 10.1007/S000140050047