标题： 面向双曲3-流形的有限刚性 显示英文标题

标题： Toward the profinite rigidity of hyperbolic 3-manifolds

摘要： 本笔记综述了关于可定向有限体积双曲3-流形的有限群刚性的最新进展。 从对有限完成和一般群刚性的基本设置的简要回顾开始，我们陈述了在3-流形分解的有限群检测以及其它类型3-流形的有限群刚性或非刚性的完整结果，这些结果将问题简化为双曲情况。 然后我们给出支持正面答案的一些证据，并总结了针对剩余双曲情况的现有思路。 我们还总结了在这一过程中使用的方法和技术。 显示英文摘要

摘要： This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the complete results in profinite detection of 3-manifold decompositions and profinite rigidity or nonrigidity of other types of 3-manifolds, which reduce the problem to the hyperbolic case. Then we give some evidence to a positive answer and conclude some existing ideas toward the remained hyperbolic case. We also summarize the methods and techniques used in the process.