Asymptotic behavior of unknotting numbers of links in a twist family

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-18 DOI:10.1016/j.topol.2025.109350

Kenneth L. Baker , Yasuyuki Miyazawa , Kimihiko Motegi

引用次数: 0

Abstract

By twisting a given link L along an unknotted circle c, we obtain an infinite family of links

{L_{n}}

. We introduce “stable unknotting number” which describes the asymptotic behavior of unknotting numbers of links in the twist family. We show the stable unknotting number for any twist family of links depends only on the winding number of L about c (the minimum geometric intersection number of L with a Seifert surface of c) and is independent of the wrapping number of L about c (the minimum geometric intersection number of L with a disk bounded by c). Thus there are twist families for which the discrepancy between the wrapping number and the stable unknotting number is arbitrarily large.

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扭转族中解结环数的渐近行为

通过将一个给定的连杆L沿着一个不打结的圆c旋转，我们得到了一个无穷一族的连杆{Ln}。引入“稳定解结数”，描述了扭转族中连杆解结数的渐近性质。我们证明了任意扭链族的稳定解结数仅取决于L关于c的圈数（L与c的塞弗特曲面的最小几何相交数），而与L关于c的缠绕数（L与以c为界的盘的最小几何相交数）无关。因此存在缠绕数与稳定解结数之间的差异任意大的扭族。

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.