论文标题
然后在缠结下
Over then Under Tangles
论文作者
论文摘要
超过（OU）缠结的缠结是面向缠结的缠结，其链穿过它们的所有过境，然后再穿过任何穿越。在本文中，我们讨论了滑行的想法：可以将任何缠结图的算法带到OU形式。不幸的是，该算法存在缺陷。但是，通过分析成功的案例，我们获得了辫子分类结果，我们也将其扩展到虚拟辫子，并提供Mathematica实现。我们讨论了其他成功的“滑行思想”的实例，这些实例出现在文献中 - 有时是伪装的 - 例如Drinfel的双重结构，Enriquez在Lie Bialgebras的量化方面的工作，Audoux和Meilhan的焊接同质链接的分类，
Over-then-Under (OU) tangles are oriented tangles whose strands travel through all of their over crossings before any under crossings. In this paper we discuss the idea of gliding: an algorithm by which any tangle diagram could be brought to OU form. Unfortunately, the algorithm is flawed. However, by analyzing cases in which it does succeed we obtain a braid classification result, which we also extend to virtual braids, and provide a Mathematica implementation. We discuss other instances of successful "gliding ideas" which appear in the literature - sometimes in disguise - such as the Drinfel'd double construction, Enriquez's work on quantization of Lie bialgebras, and Audoux and Meilhan's classification of welded homotopy links,
