随机双曲曲面上的无缠结假设
The tangle-free hypothesis on random hyperbolic surfaces
摘要：
本文引入了L-无角紧双曲曲面的概念，其灵感来自于正则图的同名性质。用Weil-Petersson概率测度选取的亏格为g的随机曲面，对于任意a < 1，都是（a log g）-无缠结的。这几乎是最优的，因为任何曲面都是（4 log g + O（1））-缠结的。我们建立了各种几何后果的纠缠自由假设在一个规模L，其中的事实，闭测地线的长度< L/4是简单的，不相交的，并嵌入在不相交的双曲柱面的宽度$\ge$ L/4。
英文摘要：
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.
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