Computation of the knot symmetric quandle and its application to the plat index of surface-links

IF 0.3 4区数学 Q4 MATHEMATICS Journal of Knot Theory and Its Ramifications Pub Date : 2024-04-30 DOI:10.1142/s0218216524500056

Jumpei Yasuda

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引用次数: 0

Abstract

A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link $F$ is a pair of a quandle and a good involution determined from $F$ . In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers $g \geq 0$ and $m \geq 2$ , there exist infinitely many distinct surface-knots of genus $g$ whose plat indices are $m$ .

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绳结对称阶数的计算及其在表面链路 plat 指数中的应用

曲面链接是嵌入 4 空间的封闭曲面，可能是断开的，也可能是不可定向的。每一个曲面链接都可以由一个编织曲面的plat closure呈现，我们称之为plat form 呈现。曲面链接 F 的结对称 quandle 是由 F 确定的一对 quandle 和一个好的反卷。作为应用，我们证明了对于任意整数 g≥0 和 m≥2，存在无穷多个不同的 g 属曲面结，其 plat 指数为 m。

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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.

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