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Automorphisms of graphs of cyclic splittings of free groups

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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.

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Acknowledgments

This work started during the programme “The Geometry of Outer space: Investigated through its analogy with Teichmueller space” held at Aix-Marseille Université during Summer 2013. We are greatly indebted to the organizers of this event. We would also like to thank Brian Mann for inspiring conversations we had there.

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  1. Université de Rennes 1, Rennes, France

    Camille Horbez & Richard D. Wade

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  1. Camille Horbez
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  2. Richard D. Wade
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Correspondence to Richard D. Wade.

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Horbez, C., Wade, R.D. Automorphisms of graphs of cyclic splittings of free groups. Geom Dedicata 178, 171–187 (2015). https://doi.org/10.1007/s10711-015-0051-2

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