论文标题
双曲线的双曲线预测和拓扑不变性
Hyperbolic projections and topological invariance of sublinearly Morse boundaries
论文作者
论文摘要
我们表明，具有因子系统的CAT（0）立方组的均匀摩尔斯山边界已明确定义，直到相对于视觉拓扑结构。证明中使用的关键工具是关于均方根摩尔斯边界的新拓扑，该拓扑是由在双曲线空间上的小组动作引起的，例如，最大的酰基辅助作用。使用相同的技术，我们可以在任何分层双曲线群体的中位数方面获得对这种新拓扑的明确描述。最后，我们使用其对低音丝带树的作用明确描述了图形歧管的均方根界边界。
We show that the sublinearly Morse boundary of a CAT(0) cubical group with a factor system is well-defined up to homeomorphism with respect to the visual topology. The key tool used in the proof is a new topology on sublinearly Morse boundaries that is induced by group actions on hyperbolic spaces that are sufficiently nice, for example, largest acylindrical actions. Using the same techniques, we obtain a explicit description of this new topology on the sublinearly Morse boundary of any hierarchically hyperbolic group in terms of medians. Finally, we explicitly describe the sublinear Morse boundaries of graph manifolds using their actions on Bass-Serre trees.
