论文标题
仿射指数多项式和Sawollek多项式
The Affine Index Polynomial and the Sawollek Polynomial
论文作者
论文摘要
本文的目的是为研究仿射指数多项式和锯片多项式的关系提供新的基础。布雷克·梅勒（Blake Mellor）写了一张开创性的纸张，以表明如何从Sawollek多项式中提取仿射指数多项式。仿射指数多项式是虚拟结的基本组合不变。 Sawollek多项式是经典亚历山大多项式的亲戚，并根据亚历山大模块对来自所谓的Alexander Biquandle的虚拟结的概括进行定义。本文为这种关系的新方法构建了基础，并简要证明了Mellor从Sawollek多项式提取仿射指数多项式的基本定理。
The purpose of this paper is to give a new basis for examining the relationships of the Affine Index Polynomial and the Sawollek Polynomial. Blake Mellor has written a pioneering paper showing how the Affine Index Polynomial may be extracted from the Sawollek Polynomial. The Affine Index Polynomial is an elementary combinatorial invariant of virtual knots. The Sawollek polynomial is a relative of the classical Alexander polynomial and is defined in terms of a generalization of the Alexander module to virtual knots that derives from the so-called Alexander Biquandle. The present paper constructs the groundwork for a new approach to this relationship, and gives a concise proof of the basic Theorem of Mellor extracting the Affine Index Polynomial from the Sawollek Polynomial.
