We prove that the generating functions for the one row/column colored HOMFLY-PT invariants of arborescent links are specializations of the generating functions of the motivic Donaldson–Thomas invariants of appropriate quivers that we naturally associate with these links. Our approach extends the previously established tangles-quivers correspondence for rational tangles to algebraic tangles by developing gluing formulas for HOMFLY-PT skein generating functions under Conway's tangle addition. As a consequence, we prove the conjectural links-quivers correspondence of Kucharski–Reineke–Stošić–Sułkowski for all arborescent links.

中文翻译：

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缠结加法和结-箭袋对应

我们证明了树状链接的一行/列彩色 HOMFLY-PT 不变量的生成函数是我们自然地与这些链接相关联的适当颤动的动机唐纳森-托马斯不变量的生成函数的特化。我们的方法通过在 Conway 的缠结加法下开发 HOMFLY-PT 绞线生成函数的粘合公式，将先前建立的有理缠结的缠结-箭袋对应扩展到代数缠结。因此，我们证明了所有树状链接的 Kucharski-Reineke-Stošić-Sułkowski 的猜想链接-箭袋对应关系。