The Whitehead link, the Borromean rings and the knot \(9_{46}\) are universal
type: Item
instance of: scholarly article
title: The Whitehead link, the Borromean rings and the knot \(9_{46}\) are universal
zbMATH Open document ID: 0554.57004
author: Hugh Michael Hilden
author: José María Montesinos-Amilibia
author: María Teresa Lozano Imízcoz
published in: Collectanea Mathematica
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/44352
review text: It is known that every closed orientable 3-manifold is obtained as an (irregular) 3-fold branched covering of some knot in \(S^ 3\). Recently, W. Thurston proved that there is a link L in \(S^ 3\) such that every closed orientable 3-manifold is some branched covering of L. Such a link L is called a universal link. The authors prove the theorem that is the title of this paper. These universal links are much simpler than Thurston's link. (Later the same authors prove that the figure-eight knot is universal which confirms Thurston's conjecture.) The proof of the theorem is geometric but ingenious.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 3883208
zbMATH Keywords: Whitehead link
zbMATH Keywords: Borromean rings
zbMATH Keywords: closed orientable 3-manifold
zbMATH Keywords: 3-fold branched covering
zbMATH Keywords: universal link
reviewed by: K. Murasugi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3883208