论文标题
属的稳定亚组两个手柄组
Stable Subgroups of the Genus Two Handlebody Group
论文作者
论文摘要
我们表明，当且仅当轨道映射到磁盘图是准等级嵌入时，且仅当属属两个手柄组的有限生成的子组才稳定。为此，我们证明了两个手柄属是一个层次上的双曲线群，并且层次结构中最大的双曲空间是对两个手柄属的磁盘图的准等级图，该磁盘构造了Hamenstädt-Hensel的构建。然后，我们利用Abbott-Behrstock-Berlyne-Durham-Russell提供的分层双曲线组的稳定亚组的表征。我们还提出了主要定理的几种应用，并表明该属的较高属类似物不存在。
We show that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a hierarchically hyperbolic group, and that the maximal hyperbolic space in the hierarchy is quasi-isometric to the disk graph of a genus two handlebody by appealing to a construction of Hamenstädt-Hensel. We then utilize the characterization of stable subgroups of hierarchically hyperbolic groups provided by Abbott-Behrstock-Berlyne-Durham-Russell. We also present several applications of the main theorems, and show that the higher genus analogues of the genus two results do not hold.
