Whitehead\(_ 3\) is a ``slice'' link
type: Item
instance of: scholarly article
title: Whitehead\(_ 3\) is a ``slice'' link
zbMATH Open document ID: 0678.57002
DOI: 10.1007/BF01394351
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143624
review text: In this paper it is shown that the Whitehead double Wh(L) of a two component link L is slice (topologically flat) if and only if the linking number of L is zero. In particular \(Wh_ 3=Wh(Wh_ 1)\) is slice. Here \(Wh_ 1\) is the Whitehead double of the Hopf link. This case acts as a marker for the general case. The slicing is obtained by building abstractly a 4-manifold with appropriate boundary and then performing surgery. This has to be done by hand rather than quoting a surgery theorem since the relevant fundamental group F(x,y) has exponential growth.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 4111597
zbMATH Keywords: Whitehead double of a two component link
zbMATH Keywords: slice links
zbMATH Keywords: linking number
zbMATH Keywords: 4- manifold
zbMATH Keywords: surgery
author: Michael Freedman
MaRDI profile type: Publication
cites work: Concordance invariance of coefficients of Conway's link polynomial
cites work: A new technique for the link slice problem
cites work: A quick proof of the 4-dimensional stable surgery theorem
cites work: Link groups
cites work: Homology and central series of groups
OpenAlex ID: W2154034657
description: scientific article; zbMATH DE number 4111597