重新审视梅尔文-莫顿-罗赞斯基扩展，或去而复返
Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
摘要：
亚历山大多项式出现在半经典的Melvin-Morton-Rozansky展开的有色纽结多项式的首项中。在这项工作中，遵循相反的方向，我们提出了如何重建有色HOMFLY-PT多项式，超多项式，和新引入的$\widehat{Z}$不变量的一些结补，从一个适当的重写，量子化和变形的亚历山大多项式。沿着这条路线，我们重新推导了最近得到的各种纽结的上述不变量的代数表达式，从而证明了它们与Melvin-Morton-Rozansky定理的一致性，并导出了以前未知的有色超多项式的新公式。对于一个给定的结，取决于某些选择，我们的重建导致等价的表达式，这要么是分圆的，或编码某些功能的HOMFLY-PT同源性和结颤抖的对应。
英文摘要：
Alexander polynomial arises in the leading term of a semi-classical Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work, following the opposite direction, we propose how to reconstruct colored HOMFLY-PT polynomials, superpolynomials, and newly introduced $\widehat{Z}$ invariants for some knot complements, from an appropriate rewriting, quantization and deformation of Alexander polynomial. Along this route we rederive conjectural expressions for the above mentioned invariants for various knots obtained recently, thereby proving their consistency with the Melvin-Morton-Rozansky theorem, and derive new formulae for colored superpolynomials unknown before. For a given knot, depending on certain choices, our reconstruction leads to equivalent expressions, which are either cyclotomic, or encode certain features of HOMFLY-PT homology and the knots-quivers correspondence.
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