H(n)移动是虚拟和焊接链路的解结操作

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-01 DOI:10.1142/s021821652350061x

Danish Ali, Zhiqing Yang, Abid Hussain, Mohd Ibrahim Sheikh

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引用次数: 0

摘要

解结操作是一种局部移动，通过这些操作的有限序列加上一些Reidemeister移动，任何结图都可以转换为平凡结的图。众所周知，H(n)移动是经典结和链的解结操作。本文将经典解结操作H(n)-move推广到虚结点和虚连杆。虚拟化和禁止移动是众所周知的解开虚拟结和链接的操作。我们还证明了虚拟化和禁止移动可以通过广义Reidemeister移动和H(n)-移动的有限序列来实现。

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The H(n)-move is an unknotting operation for virtual and welded links

An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that the H(n)-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation H(n)-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and H(n)-moves.

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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.