Presentations of automorphism groups via actions on Outer Spaces

The theory of deformation spaces of trees can be seen as an analogue, for infinite discrete groups, of representations of the group. By "twisting" the representation, one obtains an action of the deformation space itself by the automorphism group. Since these deformation spaces are usually contractible, one can study this action and its stabilisers to obtain a presentation of the automorphism groups.