粗Freundenthal紧化与群的端点
Coarse Freundenthal compactification and ends of groups
摘要：
一个真度量空间$X$的粗紧化是$X$的任何紧化，它被它的Higson紧化控制。本文描述了$X$的极大粗紧化，其冠是$0$维.在测地空间$X$的情况下，它与$X$的Freundenthal紧化一致。作为一个应用，我们提供了另一种方法，从有限生成群到任意可数群的端数的概念。本文给出了推广Stallings定理的一个几何证明，证明了任何两端可数群都包含一个有限指标的无限循环子群。最后，我们定义了任意粗糙空间的端点。
英文摘要：
A coarse compactification of a proper metric space $X$ is any compactification of $X$ that is dominated by its Higson compactification. In this paper we describe the maximal coarse compactification of $X$ whose corona is of dimension $0$. In case of geodesic spaces $X$, it coincides with the Freundenthal compactification of $X$. As an application we provide an alternative way of extending the concept of the number of ends from finitely generated groups to arbitrary countable groups. We present a geometric proof of a generalization of Stallings' theorem by showing that any countable group of two ends contains an infinite cyclic subgroup of finite index. Finally, we define ends of arbitrary coarse spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
