论文标题
重新访问Melvin-Morton-Rozansky扩展，或者再次回到
Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
论文作者
论文摘要
亚历山大多项式出现在彩色结多项式的半古典梅尔文 - 摩尔顿 - 罗赞斯基扩张的领先期间。在这项工作中，沿着相反的方向，我们建议如何重建彩色的霍姆蝇 - 多项式，超多个单位和新引入的$ \ widehat {z} $不变式，以通过适当的重写，量化，量化亚历山大·多工族的适当重写，量化和变形。沿着这条路线，我们为最近获得的各种结的上述不变性重新猜想表达式，从而证明了它们与Melvin-Morton-Rozansky Theorem的一致性，并为彩色超级分析的新公式提供了新的公式。对于给定的结（根据某些选择），我们的重建导致等效表达式，这些表达式是环形态性的，或者编码Homfly-PT同源性的某些特征和结式标语对应关系。
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.
