Mosaics for immersed surface-links

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-27 DOI:10.1016/j.topol.2024.108961

Seonmi Choi , Jieon Kim

引用次数: 0

Abstract

The concept of a knot mosaic was introduced by Lomonaco and Kauffman as a means to construct a quantum knot system. The mosaic number of a given knot K is defined as the minimum integer n that allows the representation of K on an $n \times n$ mosaic board. Building upon this, the first author and Nelson extended the knot mosaic system to encompass surface-links through the utilization of marked graph diagrams and established both lower and upper bounds for the mosaic number of the surface-links presented in Yoshikawa's table. In this paper, we establish a mosaic system for immersed surface-links by using singular marked graph diagrams. We also provide the definition and discussion on the mosaic number for immersed surface-links.

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浸入式表面连接马赛克

绳结马赛克的概念由洛莫纳科和考夫曼提出，作为构建量子绳结系统的一种手段。给定绳结的马赛克数被定义为允许在马赛克板上表示的最小整数。在此基础上，第一作者和尼尔森通过利用标记图形图表，将绳结马赛克系统扩展到包括表面链接，并建立了吉川表中表面链接马赛克数的下限和上限。在本文中，我们利用奇异标记图形图建立了浸没曲面链接的镶嵌系统。我们还给出了浸没曲面链接马赛克数的定义并进行了讨论。

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

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.