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oai:docta.ucm.es:20.500.14352/654682023-09-07T15:36:38Zcom_20.500.14352_14col_20.500.14352_21

Universal knots Hilden, Hugh Michael Lozano Imízcoz, María Teresa Montesinos Amilibia, José María Rolfsen, Dale 515.162.8 universal knot universal links Topología 1210 Topología Proceedings of a Conference held in Vancouver, Canada, June 2–4, 1983 This paper contains detailed proofs of the results in the announcement "Universal knots'' [the authors, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 449–450;]. The authors exhibit a knot K that is universal, i.e. every closed, orientable 3-manifold M can be represented as a covering of S3 branched over K, thereby giving an affirmative answer to a question of Thurston. The idea is to start with a 3-fold covering M→S3 branched over a knot and to change it to a covering M→S3 branched over a certain link L4 of four (unknotted) components. This shows that L4 is universal. Then a covering S3→S3 that is branched over a certain link L2 of two components with L4 in the preimage of L2, and a covering S3→S3 that is branched over K with L2 in the preimage of K, are constructed. This shows that L2 and K are universal. The knot K is rather complicated. In a later paper [Topology 24 (1985), no. 4, 499–504;] the authors show that the "figure eight'' knot is universal. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-21T02:43:00Z 2023-06-21T02:43:00Z 1985 book part https://hdl.handle.net/20.500.14352/65468 XXXX-XXXX 10.1007/BFb0075011 Lecture Notes in Mathematics metadata only access Springe