The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topological vertices. We discuss this interplay in the simplest example of the Hopf link and link L 8 n 8 . It turns out that the resolved conifold with four different representations on the four external legs, on the topological string side, is described by a special projection of the four-component link L 8 n 8 , which reduces to the Hopf link colored with two composite representations. Thus, this provides the first explicit example of non-torus link description through topological vertex. It is not a real breakthrough, because L 8 n 8 is just a cable of the Hopf link, still it can help to intensify the development of the formalism towards more interesting examples.
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机译：最近提出的用于结多项式的缠结演算与拓扑字符串考虑因素密切相关，可以帮助从拓扑顶点构建HOMFLY-PT不变量。我们在最简单的Hopf链接和链接L 8 n 8的示例中讨论这种相互作用。事实证明，通过四个分量链L 8 n 8的特殊投影描述了在拓扑弦侧的四个外部分支上具有四个不同表示形式的已分解轮廓，该投影简化为用两个复合材料着色的Hopf链表示形式。因此，这提供了通过拓扑顶点描述非托拉斯链接的第一个明确示例。这不是真正的突破，因为L 8 n 8只是Hopf链接的电缆，它仍然可以帮助将形式主义的发展朝着更有趣的例子发展。
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