球形结样的辫状等价

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-30 DOI:10.1016/j.topol.2025.109491

Anastasios Kokkinakis

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引用次数: 0

摘要

辫状体形成了平面结状体理论的对应理论，就像辫状体对三维连杆的作用一样。因此，平面类结图在R2中表示相同的类结图当且仅当它们可以表示为两个标记的类结图的闭包，它们之间存在等价关系，称为l -等价。在本文中，我们改进了辫状图的l -等价的概念，以得到S2中（多）-结点图在表示为标记辫状图闭包时的等价定理。

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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A braidoid equivalence for spherical knotoids

Braidoids form a counterpart theory to the theory of planar knotoids, just as braids do for three-dimensional links. As such, planar knotoid diagrams represent the same knotoid in

R^{2}

if and only if they can be presented as the closure of two labeled braidoid diagrams related by an equivalence relation, named L-equivalence. In this paper, we refine the notion of L-equivalence of braidoid diagrams in order to obtain an equivalence theorem for (multi)-knotoid diagrams in

S^{2}

when represented as the closure of labeled braidoid diagrams.

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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.