Automorphisms of graphs of cyclic splittings of free groups

Camille Horbez (1) , Richard D. Wade (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 UBC Mathematics - Department of Mathematics [Vancouver]

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.

Mots clés: Free groups; Splittings; Automorphisms of free groups; Rigidity

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]

Camille Horbez, Richard D. Wade. Automorphisms of graphs of cyclic splittings of free groups. Geometriae Dedicata, 2015, 178 (1), pp.171-187. ⟨10.1007/s10711-015-0051-2⟩. ⟨hal-01015761⟩