Publication: The Whitehead link, the Borromean rings and the knot 946 are universal.
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Publication Date
1983
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Springer
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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.
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W. Thurston. Universallinks. 1.982 (preprint).
H.Hiilden, M. Lozano and J. Montesinos. Universal knots, Bull. Amer. MatH. Soc (11) (1983),449-450.
H.Hiilden, M. Lozano and J. Montesinos. Universal knots. To arpear in Procedings of a conference held in Vancouver in 1983
U. Hirsch. "Uber offene Abbildungen auf dic 3-sphare". Mathl. Z. 140 (1.974) 203-230.
J. Montesinos. "Sobre la conjetura de Poincaré y lu~ recubridures ramificados sobre un nudo". Ph. D. Thesis, 1.971, Univcrsidad Complutense, Madrid.
J. Muntesinos. "Una nota a un Teorcma de Alexander" Revista Mat. Hisp.-Amer. 32 (1972) 167-18