It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due to the fact that reduced alternating link diagrams of the same link are obtainable from each other via flypes and flypes do not change writhe. In this paper, we introduce several quantities that are derived from Seifert graphs of reduced alternating link diagrams. We prove that they are “writhe-like” invariants, namely they are not general link invariants, but are invariants when restricted to reduced alternating link diagrams. The determination of these invariants are elementary and non-recursive so they are easy to calculate. We demonstrate that many different alternating links can be easily distinguished by these new invariants, even for large, complicated knots for which other invariants such as the Jones polynomial are hard to compute. As an application, we also derive an if and only if condition for a strongly invertible rational link.

中文翻译：

---

交替链接的类 Writhe 不变量

众所周知，从同一（交替）链路的任何简化交替链路图计算的 writhe 具有相同的值。也就是说，如果我们将自己限制在简化的交替链接图中，它就是链接不变量。这是因为同一链路的减少的交替链路图可以通过苍蝇彼此获得，并且苍蝇不会改变扭动。在本文中，我们介绍了从简化交替链接图的 Seifert 图派生的几个量。我们证明了它们是“类似扭动的”不变量，即它们不是一般的链接不变量，而是在限制于简化的交替链接图时是不变量。这些不变量的确定是基本的和非递归的，因此它们很容易计算。我们证明，这些新的不变量可以很容易地区分许多不同的交替链接，即使对于其他不变量（例如琼斯多项式）难以计算的大而复杂的节点也是如此。作为一个应用程序，我们还推导出强可逆理性链接的当且仅当条件。