纽结多项式的微分层次与附加分次
Differential hierarchy and additional grading of knot polynomials
摘要：
有色纽结多项式在某些微分组合中具有特殊的Z-展开，这取决于表示。该展开式的系数是三个变量（A，q，t）的函数，并且可以被认为是纽结多项式空间上的新的区别坐标，类似于交替特征展开式的系数。这些新的变量被分解在一个特别简单的方式，当表示被嵌入到一个产品的基本。最近在arXiv：1304.3481中提出的第四个分级，似乎只是对这些新坐标的简单重新定义，优雅但没有任何区别。如果是这样的话，它并没有提供任何新的独立的纽结不变量，相反，它可以被认为是纽结多项式背后隐藏的微分层次（Z-展开）结构的又一个证明。
英文摘要：
Colored knot polynomials possess a peculiar Z-expansion in certain combinations of differentials, which depends on the representation. The coefficients of this expansion are functions of the three variables (A,q,t) and can be considered as new distinguished coordinates on the space of knot polynomials, analogous to the coefficients of alternative character expansion. These new variables are decomposed in an especially simple way, when the representation is embedded into a product of the fundamental ones. The fourth grading recently proposed in arXiv:1304.3481, seems to be just a simple redefinition of these new coordinates, elegant but in no way distinguished. If so, it does not provide any new independent knot invariants, instead it can be considered as one more testimony of the hidden differential hierarchy (Z-expansion) structure behind the knot polynomials.
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