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.

arXiv comment22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicata

References in corpus (10)

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Cited by in corpus (3)

• Splittings of free groups from arcs and curves
• Commensurations of subgroups of $\mathrm{Out}(F_N)$
• Loxodromic elements in the cyclic splitting complex and their centralizers