Periodic knots and the skein polynomial
type: Item
instance of: scholarly article
title: Periodic knots and the skein polynomial
zbMATH Open document ID: 0753.57008
DOI: 10.1007/BF01243905
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143934
review text: The paper contains a criterion for \(p\)-periodicity of knots (\(p\) an odd prime) in terms of a regularity in the coefficients of the 2-variable polynomial. As in the case of \(p=3\) in an earlier paper, the author reduces the proof of the case of a special class of torus knots and then uses formulas available for those. As an application the question of period 5 is settled for 10-crossing knots, using in some cases refinements implying cables.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 59794
zbMATH Keywords: periodic knots
zbMATH Keywords: \(p\)-periodicity of knots
zbMATH Keywords: 2-variable polynomial
zbMATH Keywords: torus knots
zbMATH Keywords: cables
author: Paweł Traczyk
reviewed by: Gerhard Burde
MaRDI profile type: Publication
cites work: Braids and the Jones Polynomial
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cites work: Q4027122
cites work: Seifert circles and knot polynomials
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cites work: On Murasugi's and Traczyk's criteria for periodic links
cites work: Q4107635
cites work: The Jones Polynomial of Periodic Knots
OpenAlex ID: W1979097992
description: scientific article; zbMATH DE number 59794