虚拟结的交多项式Ⅱ：连通和

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2023-08-30 DOI:10.1142/s0218216523500670

Ryuji Higa, Takuji Nakamura, Yasutaka Nakanishi, S. Satoh

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引用次数: 3

摘要

我们引入了虚拟结的三种不变量，称为第一、第二和第三相交多项式。该定义基于闭合曲面上一对曲线的交点数。我们研究了相交多项式的性质及其应用，涉及对称性行为、相交数和虚拟相交数、虚拟结的连通和、相交多项式的特征、二阶有限型不变量和平面虚拟结。

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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The Intersection Polynomials of a Virtual Knot II: Connected Sums

We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study properties of the intersection polynomials and their applications concerning the behavior on symmetry, the crossing number and the virtual crossing number, a connected sum of virtual knots, characterizations of intersection polynomials, finite type invariants of order two, and a flat virtual knot.

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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.