We investigate several conjectures in geometric topology by assembling computer data obtained by studying weaving knots, a doubly infinite family W(p,n) of examples of hyperbolic knots. In particular, we compute some important polynomial knot invariants, as well as knot homologies, for the subclass W(3,n) of this family. We use these knot invariants to conclude that all knots W(3,n) are fibered knots and provide estimates for some geometric invariants of these knots. Finally, we study the asymptotics of the ranks of their Khovanov homology groups. Our investigations provide evidence for our conjecture that asymptotically as n grows large, the ranks of Khovanov homology groups of W(3,n) are normally distributed.

中文翻译：

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多项式不变量、结同调和编织结的更高捻数 W(3,n)

我们通过组装通过研究编织结获得的计算机数据来研究几何拓扑中的几个猜想，这是一个双重无限的家庭W(p,n)双曲结的例子。特别是，我们为子类计算了一些重要的多项式结不变量，以及结同调W(3,n)这个家庭的。我们使用这些结不变量来得出结论，所有结W(3,n)是纤维结，并为这些结的一些几何不变量提供估计。最后，我们研究了它们的 Khovanov 同调群的等级的渐近线。我们的调查为我们的猜想提供了证据，该猜想渐近为n变大，Khovanov 同调群的行列W(3,n)是正态分布的。