论文标题
可分散的准幕一：拓扑结束和超质性
Discretisable quasi-actions I: Topological completions and hyperbolicity
论文作者
论文摘要
我们定义并制定了可离散的准动作的概念。结果表明，在适当的非元素双曲线空间上串联的准表演$ x $不固定$ \ partial x $的点是准偶联的，即在等级一个对称空间或本地有限图上的等轴测操作。还介绍了准行动的拓扑完成。 可离散的准液体用于给出多种实例，使得通过准静态保留相称的亚组。例如，$ \ mathbb {z} $ - by-hyperbolic组的类表明是准僵化的。我们将有限生成的组类似于$ \ mathbb {z}^n \ timesγ_1$或$γ_1\ timesγ_2$，其中$γ_1$和$γ_2$是非元素超质量组。
We define and develop the notion of a discretisable quasi-action. It is shown that a cobounded quasi-action on a proper non-elementary hyperbolic space $X$ not fixing a point of $\partial X$ is quasi-conjugate to an isometric action on either a rank one symmetric space or a locally finite graph. Topological completions of quasi-actions are also introduced. Discretisable quasi-actions are used to give several instances where commensurated subgroups are preserved by quasi-isometries. For example, the class of $\mathbb{Z}$-by-hyperbolic groups is shown to be quasi-isometrically rigid. We characterise the class of finitely generated groups quasi-isometric to either $\mathbb{Z}^n\times Γ_1$ or $Γ_1\times Γ_2$, where $Γ_1$ and $Γ_2$ are non-elementary hyperbolic groups.
