Negative curvature in automorphism groups of one-ended hyperbolic groups

IF 0.6 2区 数学 Q3 MATHEMATICS
A. Genevois
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引用次数: 4

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 $\mathrm{Aut}(G)$ of a one-ended hyperbolic group $G$ turns out to be acylindrically hyperbolic. As a consequence, given a group $H$ and a morphism $\varphi : H \to \mathrm{Aut}(G)$, we deduce that the semidirect product $G \rtimes_\varphi H$ is acylindrically hyperbolic if and only if $\mathrm{ker}(H \overset{\varphi}{\to} \mathrm{Aut}(G) \to \mathrm{Out}(G))$ is finite.
单端双曲群的自同构群中的负曲率
在本文中,我们证明了当取有限生成群的自同构群时,一些负曲率可能存在。更确切地说,我们证明了单端双曲群$G$的自同构群$\mathrm{Aut}(G)$是非圆柱双曲的。因此,给定一个群$H$和一个态射$\varphi:H\to\mathrm{Aut}(G)$,我们推导出半直积$G\rtimes_\varphiH$是双曲的当且仅当$\mathrm{ker}(H\overset{\varphi}{\to}\mathrm{Aut}(G)\to\math rm{Out}(G))$是有限的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
9
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