Automorphisms of graphs of cyclic splittings of free groups

Abstract

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.

22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicata

References in corpus (1)

• Hyperbolicity of the Cyclic Splitting Complex