WHAT IS...an Acylindrical Group Action?
WHAT IS...an Acylindrical Group Action?
复制标题
什么是......非圆柱形集体行动？
DOI：
10.1090/noti1624
复制
发表时间：
2018
影响因子：
--
通讯作者：
Koberda, Thomas
中科院分区：
文献类型：
--
作者：
Koberda, Thomas
群t通过平移作用于实直线上。很难找到一个更容易理解的非平凡群作用：每个点的轨道以稳定和可预测的速度向无穷远处移动，并且群作用保留了通常的欧几里得度规。当然，这个动作是一个覆盖空间动作，这个动作的商空间是圆，完全不存在任何拓扑病态。
The group ℤ acts on the real line ℝ by translation. It is difficult to find a nontrivial group action which is easier to understand: the orbit of every point moves off to infinity at a steady and predictable rate, and the group action preserves the usual Euclidean metric on ℝ. Of course, this action is a covering space action, and the quotient space of the action is the circle, which is completely free of any topological pathologies.