Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative curvature in automorphism groups of one-ended hyperbolic groups   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.

21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn