论文标题
无限端组的自动形态群的酰基轴承双曲线
Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups
论文作者
论文摘要
我们证明，每个无限限制的有限生成的组的自动形态群都是酰基杂质的。尤其是$ \ mathrm {aut}（\ mathbb {f} _n）$对于每$ n \ ge 2 $来说都是酰基杂质。更一般而言，如果$ g $是一个几乎不是循环的组，并且相对于有限生成的适当子组的有限收集$ \ MATHCAL {p} $双曲线，则$ \ MathRM {aut}（g，\ nathcal {p}）$是酰基indrindrindrimpybybybybillicbolic。结果，当且仅当$φ$以$ \ mathrm {out}（out mathbb {f} _n）$时，仅当$ $φ$以$ \ mathrm {out mathrm {out} _n）$。
We prove that the automorphism group of every infinitely-ended finitely generated group is acylindrically hyperbolic. In particular $\mathrm{Aut}(\mathbb{F}_n)$ is acylindrically hyperbolic for every $n\ge 2$. More generally, if $G$ is a group which is not virtually cyclic, and hyperbolic relative to a finite collection $\mathcal{P}$ of finitely generated proper subgroups, then $\mathrm{Aut}(G,\mathcal{P})$ is acylindrically hyperbolic. As a consequence, a free-by-cyclic group $\mathbb{F}_n\rtimes_φ\mathbb{Z}$ is acylindrically hyperbolic if and only if $φ$ has infinite order in $\mathrm{Out}(\mathbb{F}_n)$.
