# 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…
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