Conversion to almost classical virtual links and pseudo Goeritz matrices

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-16 DOI:10.1142/s0218216522500985

Naoko Kamada

引用次数: 0

Abstract

The notion of a virtual link is a generalization of a classical link. Alexander numbering is a numbering of [Formula: see text] to arcs of a classical link diagram which is due to a numbering to disks of a complement of a link diagram in [Formula: see text]. Every classical link diagram admits Alexander numbering. A virtual link diagram corresponds to a link diagram in a closed oriented surface. Some virtual link diagrams do not admit any Alexander numbering. If a virtual link diagram admits Alexander numbering, we call it an almost classical virtual link diagram. In this paper, we construct a map from the set of virtual link diagrams to that of almost classical virtual link diagrams. It induces a map from the set of virtual links to that of almost classical virtual links. Using this map, we define a kind of Goeritz matrix of virtual link diagrams and introduce invariants of virtual links.

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转换到几乎经典的虚链接和伪格里茨矩阵

虚拟链接的概念是对经典链接的概括。亚历山大编号是[公式：见文本]对经典链接图的弧的编号，这是由于[公式：参见文本]中链接图的补码对圆盘的编号。每一个经典的链接图都允许亚历山大编号。虚拟链接图对应于封闭定向曲面中的链接图。一些虚拟链接图不允许使用任何亚历山大编号。如果一个虚拟链接图允许亚历山大编号，我们称之为几乎经典的虚拟链接图。在本文中，我们构造了一个从虚拟链接图集合到几乎经典的虚拟链接图的映射。它从一组虚拟链接导出一个映射到几乎经典的虚拟链接。利用该映射，我们定义了一类虚拟链路图的Goeritz矩阵，并引入了虚拟链路的不变量。

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.