论文标题
随机双曲表面上无缠结的假设
The tangle-free hypothesis on random hyperbolic surfaces
论文作者
论文摘要
本文介绍了无L键的紧凑双曲线表面的概念，灵感来自常规图的相同命名属性。用Weil-Petersson概率度量挑选的属G属的随机表面对于任何A <1的log G）无键。我们在尺度上建立了无缠结假设的各种几何后果，其中封闭的长度<l/4的封闭地球学是简单的，不相交的，并且嵌入了宽度宽度$ \ ge $ l/4的脱节双曲线缸中。
This article introduces the notion of L-tangle-free compact hyperbolic surfaces, inspired by the identically named property for regular graphs. Random surfaces of genus g, picked with the Weil-Petersson probability measure, are (a log g)-tangle-free for any a < 1. This is almost optimal, for any surface is (4 log g + O(1))-tangled. We establish various geometric consequences of the tangle-free hypothesis at a scale L, amongst which the fact that closed geodesics of length < L/4 are simple, disjoint and embedded in disjoint hyperbolic cylinders of width $\ge$ L/4.
