Bounding the complexity of simplicial group actions on trees

@article{Bestvina1991BoundingTC,
  title={Bounding the complexity of simplicial group actions on trees},
  author={Mladen Bestvina and Mark Feighn},
  journal={Inventiones mathematicae},
  year={1991},
  volume={103},
  pages={449-469}
}
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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