# Bounding the complexity of simplicial group actions on trees

```@article{Bestvina1991BoundingTC,
title={Bounding the complexity of simplicial group actions on trees},
journal={Inventiones mathematicae},
year={1991},
volume={103},
pages={449-469}
}```
• Published 1 December 1991
• Mathematics
• Inventiones mathematicae
We shall state the main result of this paper in terms of group actions on simplicial trees. Suppose that a group G acts simplicially on a tree T without inversions. For brevity we say that Tis a G-tree. Then the orbit space T/G is a graph whose vertices and edges correspond to G-equivalence classes of vertices and edges in T. Each vertex and edge in T/G is labeled by the stabilizer of a representative of the corresponding equivalence class. This label, a subgroup of G, is well-defined only up…
151 Citations
Branch Points and Free Actions On ℝ-Trees
Actions of groups on ℝ-trees are natural generalizations of actions of groups on ℤ-trees (simplicial trees). The latter, known as Bass-Serre Theory, has become a standard tool in combinatorial group
A Counterexample to Generalized Accessibility
• Mathematics
• 1991
Throughout this paper, G ×T → T will be an action of the group G on the tree T. Unless noted, our actions are simplicial and without inversions. In [BF], we showed that if a) G is finitely presented
Number of orbits of branch points of R-trees
An R-tree is a metric space in which any two points are joined by a unique arc. Every arc is isometric to a closed interval of R. When a group G acts on a tree (Z-tree) X without inversion, then X/G
Geometric structures on negatively curved groups and their subgroups
In this thesis, we investigate two explicit families of geometric structures that occur on hy- perbolic groups. After recalling some introductory material, we begin by giving an overview of the
Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation
• Mathematics
Israel Journal of Mathematics
• 2022
We prove that a finitely generated pro- p group G acting on a pro- p tree T splits as a free amalgamated pro- p product or a pro- p HNN-extension over an edge stabilizer. If G acts with finitely many
A fixed point theorem for deformation spaces of G-trees
For a finitely generated free group Fn, of rank at least 2, any finite subgroup of Out(Fn) can be realized as a group of automorphisms of a graph with fundamental group Fn. This result, known as
A small unstable action on a tree.
The theory of groups acting on R-trees was initiated by Tits [15] and by Alperin and Moss [1]. It was developed by Morgan and Shalen [10, 11] and others. A major advance in the theory was the
Strong accessibility for hyperbolic groups
This paper aims to give an account of theorem of Louder and Touikan [11] which shows that many hierarchies consisting of slender JSJ-decompositions are finite. In particular JSJ-hierarchies of
Deformation spaces of trees
• Mathematics
• 2006
Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the

## References

SHOWING 1-7 OF 7 REFERENCES
A Counterexample to Generalized Accessibility
• Mathematics
• 1991
Throughout this paper, G ×T → T will be an action of the group G on the tree T. Unless noted, our actions are simplicial and without inversions. In [BF], we showed that if a) G is finitely presented
Topology of finite graphs
This paper derives from a course in group theory which I gave at Berkeley in 1982. I wanted to prove the standard theorems on free groups, and discovered that, after a few preliminaries, the notion
Homological Group Theory: Topological methods in group theory
• Mathematics
• 1979
List of contributors 1. Left relatively convex subgroups Yago Antolin, Warren Dicks and Zoran Sunic 2. Groups with context-free co-word problem and embeddings into Thompson's group V Rose