On partial knots for symmetric unions

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-12 DOI:10.1016/j.topol.2025.109593

Christoph Lamm , Toshifumi Tanaka

引用次数: 0

Abstract

In this paper, we show that the partial knot of a 2-bridge ribbon knot is a 2-bridge knot. In particular, we determine the sets of partial knots for all 2-bridge ribbon knots up to 10 crossings, except for 10₃. Concerning composite symmetric unions, we show that there exists an infinite family of prime knots

{K_{m}}

such that

K_{m} ♯ - K_{m}

has at least two partial knots and we obtain symmetric union presentations for a certain family of nonsymmetric composite ribbon knots one of which was a potential counterexample to the question which asks if every ribbon knot is a symmetric union. Finally, we show that a partial knot of a symmetric union presentation with one twist region of the Kinoshita-Terasaka knot has trivial Jones polynomial.

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关于对称并集的部分节

本文证明了二桥带状结的部分结是二桥结。特别地，我们确定了所有2桥带结的部分结的集合，直到10个交叉点，除了103个。关于复合对称并，我们证明了存在一个无限族的素结{Km}使得Km #−Km至少有两个偏结，并且我们得到了一类非对称复合带状结的对称并表示，其中一个可能是“是否每个带状结都是对称并”问题的反例。最后，我们证明了Kinoshita-Terasaka结的一个扭转区域的对称并表示的部分结具有平凡的Jones多项式。

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.