Stable actions of groups on real trees

@article{Bestvina1995StableAO,
  title={Stable actions of groups on real trees},
  author={Mladen Bestvina and Mark Feighn},
  journal={Inventiones mathematicae},
  year={1995},
  volume={121},
  pages={287-321}
}
This paper further develops Rips's work on real trees. We study a class of actions called ‘stable’ which includes actions with trivial arc stabilizers and small actions of hyperbolic groups. 
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References

SHOWING 1-10 OF 14 REFERENCES
Outer Automorphisms of Hyperbolic Groups and Small Actions on ℝ-Trees
If Γ is a group, denote by Out(Γ) the group of outer automorphisms of Γ. The definitions of the notions used in this introduction are given in the first section. The main theorem of this paper
ON SYSTEMS OF EQUATIONS IN A FREE GROUP
A description of the general solution of given bounded periodicity exponent is obtained for an arbitrary system of equations in a free group. On the basis of this result an algorithm is constructed
EQUATIONS IN A FREE GROUP
An algorithm for recognizing the solvability of arbitrary equations in a free group is constructed. Bibliography: 11 titles.
Moduli of graphs and automorphisms of free groups
This paper represents the beginning of an a t tempt to transfer, to the study of outer au tomorphisms of free groups, the powerful geometric techniques that were invented by Thurs ton to study
Dendrology of Groups: An Introduction
TLDR
The study of group actions on “generalized trees” or “ℝ-trees” has recently been attracting the attention of mathematicians in several different fields and has been developed further by the above-mentioned people and also by H. Culler, H. Gillet, M. Rimlinger and J. Stallings.
Degenerations of hyperbolic structures, II: Measured laminations in 3-manifolds
That paper concerned the general theory of groups acting on R-trees and the relationship of these actions to representations into SL2(C). The purpose of the present paper is to develop the
$\Lambda $\<-Trees and Their Applications
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of
Topologie de Gromov équivariante, structures hyperboliques et arbres réels
RésuméLes objets que nous étudions sont les espaces métriques munis d'une action par isométrie d'un groupe fixé Γ. Nous définissons une «topologie» naturelle sur «l'ensemble» de ces espaces. Nous
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