用Haar测度重新讨论Leighton定理
Revisiting Leighton's Theorem with the Haar Measure
摘要：
莱顿的图覆盖定理指出，一对具有同构泛覆盖的有限图有一个公共的有限覆盖。我们提供了一个新的证明莱顿定理，允许推广，我们证明了相应的结果与鳍图。作为一个推论，我们得到的自由群的模式刚性与线模式，建立在工作的Cashen-Macura和哈根-Touikan。为了说明未来的应用潜力，我们给出了自由群的循环双族的拟等距刚性结果。
英文摘要：
Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that allows generalizations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen-Macura and Hagen-Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.
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。
