• DOI:10.1007/BF01239522
• Corpus ID: 121136037

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}
}

• M. Bestvina, Mark Feighn
• 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 to conjugation in G (for details, see [7] or [8]). Thus T/G is a graph of groups whose fundamental group is G. We are interested in finding a number ?(G), depending only on G, so that for every G-tree T, the graph T/G has no more than ?(G) vertices and edges. Some remarks are in order.