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Geometriae Dedicata

, Volume 178, Issue 1, pp 171–187 | Cite as

Automorphisms of graphs of cyclic splittings of free groups

  • Camille Horbez
  • Richard D. WadeEmail author
Original Paper

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.

Keywords

Free groups Splittings Automorphisms of free groups Rigidity 

Mathematics Subject Classification

20E36 20F65 (Primary) 20E05 20E08 

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Université de Rennes 1RennesFrance

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