### Impacto

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

## Abstract

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 |
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Subjects: | Sciences > Mathematics > Topology |

ID Code: | 17185 |

References: | R. H. Fox: A quick trip through knot theory. Topology of 3-manifolds and Related Topics. Prentice-Hall:Englewood Cliffs (1962). C. MCA. Gordon and W. Heil: Simply connected branched coverings of S’. Proc. Am. Math. Sot. 35 (1972), 287-288. A. Hatcher and W. Thurston: Incompressible surfaces in 2-bridge knot complements. fnuent. Math. (to appear). H. M. Hilden, M . T. Lozano and J. M. Montesinos:The Whitehead link, the Borromean ringsand the knot 946 are universal, Collectanea Mathematica, XXXIV (1983), pp. 19–28. H. Schubertk: Knoten mit zwei Brücken. Math. Z. 65 (1956), 133-170. W. Thurstonu: Universal links. (preprint, 1982). |

Deposited On: | 23 Nov 2012 11:41 |

Last Modified: | 07 Feb 2014 09:43 |

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