Negative curvature in automorphism groups of one-ended hyperbolic groups

  • Anthony Genevois

    Université Paris-Sud, Orsay, France
Negative curvature in automorphism groups of one-ended hyperbolic groups cover
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Abstract

In this article, we show that some negative curvature may survive when taking the automorphism group of a finitely generated group. More precisely, we prove that the automorphism group Aut(G)\mathrm{Aut}(G) of a one-ended hyperbolic group GG turns out to be acylindrically hyperbolic. As a consequence, given a group HH and a morphism φ:HAut(G)\varphi : H \to \mathrm{Aut}(G), we deduce that the semidirect product GφHG \rtimes_\varphi H is acylindrically hyperbolic if and only if ker(HφAut(G)Out(G))\mathrm{ker}(H \overset{\varphi}{\to} \mathrm{Aut}(G) \to \mathrm{Out}(G)) is finite.

Cite this article

Anthony Genevois, Negative curvature in automorphism groups of one-ended hyperbolic groups. J. Comb. Algebra 3 (2019), no. 3, pp. 305–329

DOI 10.4171/JCA/33