## Moduli of graphs and automorphisms of free groups.(English)Zbl 0589.20022

From the author’s introduction: ”This paper represents the beginning of an attempt to transfer, to the study of outer automorphisms of free groups, the powerful geometric techniques that were invented by Thurston to study mapping classes of surfaces. Let $$F_ n$$ denote the free group of rank n. We will study the group $$Out(F_ n)$$ of outer automorphisms of $$F_ n$$ by studying its action on a space $$X_ n$$ which is analogous to the Teichmüller space of hyperbolic metrics on a surface; the points of $$X_ n$$ are metric structures on graphs with fundamental group $$F_ n.''$$ The main result of this paper is that the space $$X_ n$$ is contractible. This has as a corollary that the group $$Out(F_ n)$$ has virtual cohomological dimension 2n-3.