The symmetries of Outer space

Martin R. Bridson and Karen Vogtmann

Duke Math. J., vol 106 (2001), 391--409

For $n\geq 3$, the natural map $Out(F_n)\to Aut(K_n)$ from the outer automorphism group of the free group of rank n to the group of simplicial automorphisms of the spine of outer space is an isomorphism.

Figure 6