The Jones polynomial for a torus knot with twists

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-09-11 DOI:10.1016/j.topol.2024.109069

Brandon Bavier , Brandy Doleshal

引用次数: 0

Abstract

We compute the Jones polynomial for a three-parameter family of links, the twisted torus links of the form $T ((p, q), (2, s))$ where p and q are coprime and s is nonzero. When $s = 2 n$ , these links are the twisted torus knots $T (p, q; 2, n)$ . We show that for $T (p, q; 2, n)$ , the Jones polynomial is trivial if and only if the knot is trivial.

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带捻环结的琼斯多项式

我们计算了一个三参数链节族的琼斯多项式，即 T((p,q),(2,s))形式的扭曲环链节，其中 p 和 q 是共素数，s 是非零。当 s=2n 时，这些链接就是扭曲环结 T(p,q;2,n)。我们将证明，对于 T(p,q;2,n)，如果且只有当结是琐碎的，琼斯多项式才是琐碎的。

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.