On knots that are universal



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Montesinos Amilibia, José María and Hilden, Hugh Michael and Lozano Imízcoz, María Teresa (1985) On knots that are universal. Topology. An International Journal of Mathematics, 24 (4). pp. 49-504. ISSN 0040-9383

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Official URL: http://www.sciencedirect.com/science/article/pii/0040938385900199


The authors construct a cover S3→S3 branched over the "figure eight" knot with preimage the "roman link" and a cover S3→S3 branched over the roman link with preimage containing the Borromean rings L. Since L is universal (i.e. every closed, orientable 3-manifold can be represented as a covering of S3 branched over L) it follows that the "figure eight'' knot is universal, thereby answering a question of Thurston in the affirmative. More generally, it is shown that every rational knot or link which is not toroidal is universal

Item Type:Article
Subjects:Sciences > Mathematics > Topology
ID Code:17185
Deposited On:23 Nov 2012 11:41
Last Modified:12 Dec 2018 15:14

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