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On hyperbolicity and virtual freeness of automorphism groups

Geometriae Dedicata volume 207, pages 51–60 (2020)Cite this article

Abstract

We show that word hyperbolicity of automorphism groups of graph products \(G_\Gamma \) and of Coxeter groups \(W_\Gamma \) depends strongly on the shape of the defining graph \(\Gamma \). We also characterize those \(\mathrm{Aut}(G_\Gamma )\) and \(\mathrm{Aut}(W_\Gamma )\) in terms of \(\Gamma \) that are virtually free.

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Notes

  1. For definition see 3.1.

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Acknowledgements

The author thanks the referee for careful reading of the manuscript and many helpful remarks.

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  1. Department of Mathematics, Münster University, Einsteinstraße 62, 48149, Münster, Germany

    Olga Varghese

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  1. Olga Varghese
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Correspondence to Olga Varghese.

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Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Münster: Dynamics-Geometry-Structure.

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Varghese, O. On hyperbolicity and virtual freeness of automorphism groups. Geom Dedicata 207, 51–60 (2020). https://doi.org/10.1007/s10711-019-00486-6

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