Concordance invariance of coefficients of Conway's link polynomial
type: Item
instance of: scholarly article
title: Concordance invariance of coefficients of Conway's link polynomial
zbMATH Open document ID: 0589.57005
DOI: 10.1007/BF01388868
author: Tim D. Cochran
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143298
review text: The Conway polynomial of a link in \(S^ 3\) is an invariant of the isotopy class of the link, and is related to the classical Alexander polynomial by a change of variable and a normalization. An important problem is to determine which data of this polynomial are cobordism invariants, i.e. are invariant under concordance of links. The author shows that the first non-vanishing coefficient, as well as the mod 2 reduction of the next coefficient, of this polynomial are invariant under link concordance. For 2- and 3-component links, he also gives a geometric interpretation of this first non-vanishing coefficient. He also obtains similar results for the mod 2 reduction of the Conway polynomial and for the 2-variable polynomial introduced by \textit{P. Freyd} et al. [Bull. Am. Math. Soc. 12, 239-246 (1985; Zbl 0572.57002)].
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 3947217
zbMATH Keywords: Conway polynomial of a link
zbMATH Keywords: Alexander polynomial
zbMATH Keywords: cobordism invariants
zbMATH Keywords: concordance of links
zbMATH Keywords: 2- and 3-component links
reviewed by: Francis Bonahon
MaRDI profile type: Publication
cites work: Link Cobordism and Milnor's Invariant
cites work: Geometric invariants of link cobordism
cites work: Q5601331
cites work: Singularities of 2-spheres in 4-space and cobordism of knots
cites work: A new polynomial invariant of knots and links
cites work: A Family of Links and the Conway Calculus
cites work: Alexander Ideals and Chen Groups
cites work: Alexander ideals of links
cites work: The Conway potential function for links
cites work: The First Coefficient of the Conway Polynomial
cites work: The Arf invariant of a totally proper link
cites work: A polynomial invariant for knots via von Neumann algebras
cites work: The Conway polynomial
cites work: On the Alexander polynomials of cobordant links
cites work: The New Polynomial Invariants of Knots and Links
cites work: Link groups
cites work: Q3247621
cites work: Q3726995
cites work: On the Arf invariant of links
cites work: On Milnor's Invariant for Links. II. The Chen Group
cites work: On the Alexander polynomials of slice links
cites work: An invariant of knot cobordism
cites work: Q4107635
cites work: Isotopy Invariants of Links and The Alexander Matrix
cites work: Milnor's Invariants and the Completions of Link Modules
cites work: Q5586064
description: scientific article; zbMATH DE number 3947217