The Whitehead link, the Borromean rings and the knot 946 are universal.

Hugh M. Hilden; María Teresa Lozano; José María Montesinos

Collectanea Mathematica (1983)

  • Volume: 34, Issue: 1, page 19-28
  • ISSN: 0010-0757

Abstract

top
A link L in S3 is universal if every closed, orientable 3-manifold is a covering of S3 branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot remains open, but we show that the ribbon knot 946 is universal.

How to cite

top

Hilden, Hugh M., Lozano, María Teresa, and Montesinos, José María. "The Whitehead link, the Borromean rings and the knot 946 are universal.." Collectanea Mathematica 34.1 (1983): 19-28. <http://eudml.org/doc/44352>.

@article{Hilden1983,
abstract = {A link L in S3 is universal if every closed, orientable 3-manifold is a covering of S3 branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot remains open, but we show that the ribbon knot 946 is universal. },
author = {Hilden, Hugh M., Lozano, María Teresa, Montesinos, José María},
journal = {Collectanea Mathematica},
keywords = {3-variedades; Enlace universal; Variedad recubridora; Transposición; Whitehead link; Borromean rings; closed orientable 3-manifold; 3-fold branched covering; universal link},
language = {eng},
number = {1},
pages = {19-28},
title = {The Whitehead link, the Borromean rings and the knot 946 are universal.},
url = {http://eudml.org/doc/44352},
volume = {34},
year = {1983},
}

TY - JOUR
AU - Hilden, Hugh M.
AU - Lozano, María Teresa
AU - Montesinos, José María
TI - The Whitehead link, the Borromean rings and the knot 946 are universal.
JO - Collectanea Mathematica
PY - 1983
VL - 34
IS - 1
SP - 19
EP - 28
AB - A link L in S3 is universal if every closed, orientable 3-manifold is a covering of S3 branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot remains open, but we show that the ribbon knot 946 is universal.
LA - eng
KW - 3-variedades; Enlace universal; Variedad recubridora; Transposición; Whitehead link; Borromean rings; closed orientable 3-manifold; 3-fold branched covering; universal link
UR - http://eudml.org/doc/44352
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.