Alexander polynomials of simple-ribbon knots
type: Item
instance of: scholarly article
title: Alexander polynomials of simple-ribbon knots
author: Kengo Kishimoto
author: Tetsuo Shibuya
author: Tatsuya Tsukamoto
author: Tsuneo Ishikawa
published in: Osaka Journal of Mathematics
publication date: 2021-08-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1905.04915
full work available at URL: euclid.5150ojm
review text: In a previous work, the authors introduced special types of fusions, so called simple-ribbon fusions on links. Every simple-ribbon fusion can be realized by ``elementary'' simple-ribbon fusions. A knot obtained from the trivial knot by a finite sequence of simple-ribbon fusions is called a simple-ribbon knot. Every ribbon knot with \(\leq 9\) crossings is a simple-ribbon knot. An \(m\)-simple-ribbon knot is a knot obtained from the trivial one by a finite sequence of elementary \(m\)-simple-ribbon fusions for a fixed positive integer \(m\). In this paper, the authors give a formula for the Alexander polynomials of simple-ribbon knots. As an application, they determine if a knot with \(10\) crossings is a simple-ribbon knot. Moreover, they provide a condition for a simple-ribbon knot to be both of an \(m\)-simple-ribbon knot and an \(n\)-simple-ribbon knot for positive integers \(m\) and \(n\).
reviewed by: Leila Ben Abdelghani
Mathematics Subject Classification ID: 57K10
Mathematics Subject Classification ID: 57K14
zbMATH DE Number: 7383195
zbMATH Keywords: ribbon knot
zbMATH Keywords: ribbon fusion
zbMATH Keywords: Alexander polynomial
zbMATH Keywords: Seifert surface
MaRDI profile type: Publication
cites work: Knots
cites work: On Prime Factors of A n - 1
cites work: Q4845496
cites work: Simple ribbon fusions and genera of links
cites work: Q5855380
cites work: Primary cyclotomic units and a proof of Catalans conjecture
cites work: Knoten und Vollringe
cites work: Q3902187
description: scientific article; zbMATH DE number 7383195