论文标题
有限学位覆盖的统计数据
Statistics of finite degree covers of torus knot complements
论文作者
论文摘要
在本文的第一部分中，我们确定了圆环结的基本组的渐近亚组生长。在第二部分中，我们使用它来研究圆环结互补的随机有限程度覆盖物。我们确定了他们的本杰米尼 - 施拉姆限制和这些覆盖物的贝蒂数量的线性生长速率。所有这些结果概括为$ \ mathrm {psl}（2，\ mathbb {r}）\ times \ times \ mathbb {r} $中的较大类晶格。作为我们证明的副产品，我们获得了与扭转的高度随机覆盖的高度随机覆盖物的类似极限定理。
In the first part of this paper, we determine the asymptotic subgroup growth of the fundamental group of a torus knot complement. In the second part, we use this to study random finite degree covers of torus knot complements. We determine their Benjamini-Schramm limit and the linear growth rate of the Betti numbers of these covers. All these results generalise to a larger class of lattices in $\mathrm{PSL}(2,\mathbb{R})\times \mathbb{R}$. As a by-product of our proofs, we obtain analogous limit theorems for high degree random covers of non-uniform Fuchsian lattices with torsion.
