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

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1983) The Whitehead link, the Borromean rings and the knot 946 are universal. Collectanea mathematica, 34 (1). pp. 19-28. ISSN 0010-0757

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Official URL: http://www.collectanea.ub.edu/index.php/Collectanea/article/view/3575/4254




Abstract

W. Thurston proved the existence of universal links L⊂S3 which are defined by the property that every closed orientable 3-manifold is a branched covering over L⊂S3. The authors answered earlier [Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 3, 449–450;] Thurston's question of whether there are universal knots in the affirmative. In the paper under review, they start from the fact that every closed orientable 3-manifold is an irregular 3-fold covering over a negative closed braid, and proceed by changing the braid by certain moves which do not alter the covering manifold. Thus they arrive at the conclusion that the Whitehead link, the Borromean rings and the knot 946 are universal. Whether the figure-eight knot is universal remains an open question.


Item Type:Article
Uncontrolled Keywords:Borromean rings;
Subjects:Sciences > Mathematics > Topology
ID Code:22051
Deposited On:21 Jun 2013 16:21
Last Modified:12 Dec 2018 15:14

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