Deformation spaces of trees

  • Vincent Guirardel

    Université de Rennes 1, Rennes, France
  • Gilbert Levitt

    Université de Caen Basse-Normandie, Caen, France


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 other). Examples include Culler–Vogtmann's outer space and spaces of JSJ decompositions. We discuss what features are common to trees in a given deformation space, how to pass from one tree to all other trees in its deformation space, and the topology of deformation spaces. In particular, we prove that all deformation spaces are contractible complexes.

Cite this article

Vincent Guirardel, Gilbert Levitt, Deformation spaces of trees. Groups Geom. Dyn. 1 (2007), no. 2, pp. 135–181

DOI 10.4171/GGD/8