Small difference between tunnel numbers of cable knots and their companions

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-09-04 DOI:10.1016/j.topol.2024.109058

Junhua Wang , Wenjie Diao , Yanqing Zou

引用次数: 0

Abstract

We prove that for any nontrivial knot $K \subset S^{3}$ and a $p / q$ -cable knot $K^{⋆}$ of K, the tunnel number $t (K) = t (K^{⋆})$ if and only if K is $p / q$ -primitive. This result solves a problem mentioned in [8].

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缆结隧道数与同伴数之间的微小差异

我们证明，对于任何非琐结 K⊂S3 和 K 的 p/q-cable 结 K⋆，当且仅当 K 是 p/q-primitive 时，隧道数 t(K)=t(K⋆) 。这一结果解决了 [8] 中提到的一个问题。

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.