论文标题
交替链接的类似不变的
Writhe-like invariants of alternating links
论文作者
论文摘要
众所周知，从同一（交替）链接的任何简化的交替链路图计算得出的扭曲。也就是说，如果我们将自己限制为减少交替的链路图，则是链接不变的。这是由于以下事实：相同链路的交替链路图还可以通过飞台和飞台彼此获得，不会改变旋转。在本文中，我们介绍了从还原的交替链路图的Seifert图中得出的几个数量。我们证明它们是“旋转”不变的，因为它们也是降低的交替链路图中的链接不变性。这些不变性的确定是基本的和非恢复性的，因此很容易计算。我们证明，这些新的不变式很容易区分许多不同的交替链接，即使对于大型，复杂的结，其他不变的结（例如琼斯多项式）也很难计算。作为一个应用程序，我们还出于强烈可逆的有理链接的条件而得出一个。
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 in the sense that they are also link invariants among 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.
