一个用于排除纠缠双曲曲面的默比乌斯反演公式
A Moebius inversion formula to discard tangled hyperbolic surfaces
AI总结：
本文提出一个 Moebius 反演公式，系统处理 Weil-Petersson 随机双曲曲面中的无纠缠条件，并证明该假设将短测地线局部拓扑类型的指数增长降为多项式增长。
摘要：
近期关于 Weil-Petersson 随机双曲曲面的文献遇到了一个持续的障碍：必须对模型进行条件化，禁止某些罕见的几何模式（我们称之为纠缠（tangles）），例如短的闭合测地线或具有短边界长度的嵌入曲面。本文的主要成果是一个 Moebius 反演公式，允许以系统且易于处理的方式对无纠缠曲面集合的指示函数进行积分。它受 Friedman 对 Alon 猜想的著名证明中的关键步骤启发。我们进一步证明，我们的无纠缠假设显著减少了短测地线的局部拓扑类型数量，将纠缠曲面上观察到的指数级激增替换为多项式增长。
英文摘要：
Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (which we call tangles), such as short closed geodesics or embedded surfaces of short boundary length. The main result of this article is a Moebius inversion formula, allowing to integrate the indicator function of the set of tangle-free surfaces in a systematic, tractable way. It is inspired by a key step of Friedman's celebrated proof of Alon's conjecture. We further prove that our tangle-free hypothesis significantly reduces the number of local topological types of short geodesics, replacing the exponential proliferation observed on tangled surfaces by a polynomial growth.
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。
