JournalscmhVol. 73 , No. 1DOI 10.1007/s000140050047

Approximations of stable actions on R \Bbb {R} -trees

  • Vincent Guirardel

    Université de Rennes 1, Rennes, France
Approximations of stable actions on $ \Bbb {R} $-trees cover


This article shows how to approximate a stable action of a finitely presented group on an R\Bbb {R} -tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an R\Bbb {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 R\Bbb {R} -trees and on the dynamical study of exotic components by D. Gaboriau.