有理3-缠结的正规形式

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-08 DOI:10.1016/j.topol.2025.109388

Bo-hyun Kwon , Jung Hoon Lee

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引用次数: 0

摘要

在Σ0,6中适当嵌入三个不相交的简单弧线的集合表示一个合理的3-缠结。对于给定的有理3-缠结，我们定义了三个不相交桥弧集合的正规形式。我们证明了有一个称为正常跳跃移动的操作序列，它在同一有理3缠结的正常形式集中的任意两个元素之间形成了一条路径。我们认为，范式将为理性3-缠结的分类提供线索。

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Normal forms for rational 3-tangles

A collection of properly embedded three disjoint simple arcs in

Σ_{0, 6}

represents a rational 3-tangle. In this paper, we define a normal form of collections of three disjoint bridge arcs for a given rational 3-tangle. We show that there is a sequence of operations called normal jump moves which makes a path between arbitrary two elements in the set of normal forms of the same rational 3-tangle. We believe that the normal form would give a clue to classify rational 3-tangles.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.