发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过ribbon范畴方法，刻画了闭2-orbifold随机覆盖的小尺度典型结构，推广了Magee和Puder的结果至不可定向情形，并回答了Puder和Zimhoni的问题。
AI 中文摘要
我们描述了闭2-orbifold的典型覆盖在小尺度上的样子。具体而言，我们证明了一个均匀随机覆盖的度数n在期望中包含Θ(n^0)条短闭测地线，可能有Θ(n^0)对邻近的2阶锥点，一般有Θ(n^{1/m})个m阶锥点，并且以高概率没有具有更复杂拓扑的小区域。这推广了Magee和Puder（2023）的许多结果，从可定向曲面推广到可能不可定向的orbifold，并回答了Puder和Zimhoni（2024）提出的一些问题。
英文摘要
We describe what a typical covering of a closed 2-orbifold looks like on a small scale. Specifically, we prove that a uniformly random covering of degree n contains in expectation $Θ(n^0)$ short closed geodesics, potentially $Θ(n^0)$ pairs of nearby order-2 cone points, in general $Θ(n^{\frac{1}{m}})$ cone points of order m, and with high probability no small regions with more complicated topology. This generalises many results of Magee and Puder (2023) from orientable surfaces to possibly non-orientable orbifolds, and answers some of the questions raised by Puder and Zimhoni (2024).
