Extending quasi-alternating links III

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-16 DOI:10.1016/j.topol.2026.109736

Kirandeep Kaur , Nafaa Chbili

引用次数: 0

Abstract

Champanerkar and Kofman [1] introduced a method for constructing quasi-alternating links by replacing a quasi-alternating crossing in a link diagram with a rational tangle of the same type. This approach, however, does not generally extend to alternating tangles of the opposite type or to non-alternating tangles.

In this paper, we identify sufficient conditions under which the construction remains valid when the crossing is replaced by an alternating rational tangle of opposite type. We also prove that this method applies to certain non-alternating pretzel tangles. As an application, we provide a table of non-alternating quasi-alternating knots with 13 crossings obtained using this construction. Additionally, we describe an infinite family of quasi-alternating links featuring a non-twisted quasi-alternating crossing that satisfies these sufficient conditions.

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扩展拟交替连杆III

Champanerkar和Kofman等人提出了一种构造准交替链路的方法，即用同类型的有理缠结代替链路图中的准交替交叉。然而，这种方法通常不适用于相反类型的交替缠结或非交替缠结。在本文中，我们确定了当交叉被相反类型的交替理性缠结取代时结构仍然有效的充分条件。我们还证明了该方法适用于某些非交替的椒盐卷饼缠结。作为应用，我们给出了用这种构造得到的具有13个交点的非交变准交变结表。此外，我们还描述了满足这些充分条件的具有非扭曲拟交变交叉的无限族拟交变链路。

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.