Conway polynomial and oriented rotant links
type: Item
instance of: scholarly article
title: Conway polynomial and oriented rotant links
zbMATH Open document ID: 1081.57007
published in: Geometriae Dedicata
publication date: 2005-05-04T00:00:00Z
review text: This paper gives a positive answer to the question, raised in [\textit{G. T. Jin} and \textit{D. Rolfsen}, Can. Math. Bull., 34, 480--484 (1991; Zbl 0754.57002)], of whether the Conway polynomials agree for oriented \(n\)-rotants of all orders \(n\). A pair of links \(L_1\) and \(L_2\) are called oriented rotants of order \(n\) if \(L_2\) has a diagram obtained from that of \(L_1\) in the following way: let \(R_1\) be the part of the diagram of \(L_1\) contained in a disk \(B\) and invariant under a rotation by angle \(2\pi/n\); the diagram of \(L_2\) is obtained by rotating \(R_1\) by \(\pi\) through the space around an axis lying on the plane of the diagram and reversing all orientations of the strings on \(R_1\). The author proves that the Conway polynomials of a pair of oriented rotants of any order coincide. The idea of the proof is to translate the topological problem into one of linear algebra. More precisely, the equality of the Conway polynomials follows from the equality of the determinants of certain Hermitian matrices associated with the Conway potential.
reviewed by: Luigi Grasselli
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 2165502
zbMATH Keywords: Conway polynomial
zbMATH Keywords: rotants
author: Paweł Traczyk
MaRDI profile type: Publication
full work available at URL: s10711-004-5793-1
OpenAlex ID: W1999570752
cites work: Knot polynomials and generalized mutation
cites work: Some Remarks on Rotors in Link Theory
cites work: The homfly and the Kauffman bracket polynomials for the generalized mutant of a link
cites work: COMMUTING TRANSFER MATRICES AND LINK POLYNOMIALS
cites work: GLOBAL MUTATION OF KNOTS
cites work: Q4863284
cites work: A NOTE ON ROTANT LINKS
cites work: Tangle Surgeries Which Preserve Jones-Type Polynomials
DOI: 10.1007/S10711-004-5793-1
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description: scientific article; zbMATH DE number 2165502