仿射指数多项式与Sawollek多项式

L. Kauffman
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引用次数: 3

摘要

本文的目的是为研究仿射指数多项式和Sawollek多项式之间的关系提供一个新的基础。Blake Mellor写了一篇开创性的论文,展示了如何从Sawollek多项式中提取仿射指数多项式。仿射指数多项式是虚节的初等组合不变量。Sawollek多项式是经典Alexander多项式的一个相关项,它是根据Alexander模对虚节的推广来定义的,虚节源于所谓的Alexander Biquandle。本文为研究这一关系的新方法奠定了基础,并给出了从Sawollek多项式中提取仿射指数多项式的Mellor基本定理的简明证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Affine Index Polynomial and the Sawollek Polynomial
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.
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