Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2023-06-02 DOI:10.1142/s0218216523500840

Butian Zhang

引用次数: 0

Abstract

A state model for Kauffman polynomial of Dubrovnik-version is given. Based on the state model, the Gauss diagram formulae for Vassiliev invariants are given from the coefficients of Kauffman polynomial following the method of Chmutov and Polyak. Some arrow diagram identities are given to simplify the Gauss diagram formulae of order 3, which give Polyak-Viro and Chmutov-Polyak formulae for the Vassiliev invariant of order 3. The models of Kauffman polynomial and HOMFLY-PT polynomial give different Gauss diagram expressions when specializing to Jones poynomial.

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来自考夫曼多项式的瓦西里耶夫不变式的高斯图公式

给出了杜布罗夫尼克版考夫曼多项式的状态模型。根据该状态模型，按照 Chmutov 和 Polyak 的方法，从考夫曼多项式系数给出了瓦西里耶夫不变式的高斯图公式。给出了一些箭头图同义来简化阶 3 的高斯图公式，从而给出了阶 3 的瓦西里耶夫不变量的 Polyak-Viro 和 Chmutov-Polyak 公式。考夫曼多项式和 HOMFLY-PT 多项式的模型在特殊化为琼斯多项式时给出了不同的高斯图表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Knot Theory and Its Ramifications 数学-数学

CiteScore

0.80

自引率

40.00%

发文量

127

审稿时长

4-8 weeks

期刊介绍： This Journal is intended as a forum for new developments in knot theory, particularly developments that create connections between knot theory and other aspects of mathematics and natural science. Our stance is interdisciplinary due to the nature of the subject. Knot theory as a core mathematical discipline is subject to many forms of generalization (virtual knots and links, higher-dimensional knots, knots and links in other manifolds, non-spherical knots, recursive systems analogous to knotting). Knots live in a wider mathematical framework (classification of three and higher dimensional manifolds, statistical mechanics and quantum theory, quantum groups, combinatorics of Gauss codes, combinatorics, algorithms and computational complexity, category theory and categorification of topological and algebraic structures, algebraic topology, topological quantum field theories). Papers that will be published include: -new research in the theory of knots and links, and their applications; -new research in related fields; -tutorial and review papers. With this Journal, we hope to serve well researchers in knot theory and related areas of topology, researchers using knot theory in their work, and scientists interested in becoming informed about current work in the theory of knots and its ramifications.