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On hyperbolicity and virtual freeness of automorphism groups


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

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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).

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