环绕数与Conway多项式低次系数的组合Goussarov-Polyak-Viro公式
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
中文总结 AI 辅助
本文利用基本线性代数，以Gauss图向量空间的基显式描述了环绕数和Conway多项式低次系数的GPV映射，提供了一种更基础的计算方法。
中文摘要 AI 辅助
环绕数和Conway多项式的系数是有限型不变量的两个例子。Goussarov-Polyak-Viro证明了任何有限型纽结不变量都可以通过两步过程计算，其中第二步被称为该不变量的GPV映射。本文计算了环绕数和Conway多项式低次系数的GPV映射。Chmutov-Khoury-Rossi用箭头图和状态和计算给出了Conway多项式系数的GPV映射的一种描述。我们采用更基础的方法，利用基本线性代数，以Gauss图向量空间的基来描述GPV映射。
英文摘要
The linking number and coefficients of the Conway polynomial are two examples of finite type invariants. Goussarov-Polyak-Viro proved that any finite type knot invariant can be computed in a two step process, where the second step is referred to as the GPV map for the invariant. This paper computes the GPV maps for the linking number and low-degree coefficients of the Conway Polynomial. Chmutov-Khoury-Rossi gave one description of the GPV maps for coefficients of the Conway polynomial in terms of arrow diagrams and state-sum calculations. We take a much more grounded approach using fundamental linear algebra to describe the GPV maps in terms of a basis for the vector space of Gauss diagrams.
