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Hyperbolicity of the cyclic splitting graph

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Abstract

We define a new graph on which \(Out(F_n)\) acts by simplicial automorphisms, the cyclic splitting graph of \(F_n\), and show that \(FZ_n\) is hyperbolic using a method developed by Kapovich and Rafi (Hyperbolicity of the free factor complex, 2012).

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Acknowledgments

The author thanks Mladen Bestvina, Kasra Rafi, and Patrick Reynolds for their immense patience and for enlightening conversations. He also thanks Sam Taylor for helpful comments on the first draft.

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  1. Department of Mathematics, University of Utah, 155 S 1400 E, Room 233, Salt Lake City, UT, 84112, USA

    Brian Mann

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  1. Brian Mann
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Correspondence to Brian Mann.

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Mann, B. Hyperbolicity of the cyclic splitting graph. Geom Dedicata 173, 271–280 (2014). https://doi.org/10.1007/s10711-013-9941-3

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  • DOI: https://doi.org/10.1007/s10711-013-9941-3

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