RT Book, Section
T1 Universal knots
A1 Hilden, Hugh Michael
A1 Lozano Imízcoz, María Teresa
A1 Montesinos Amilibia, José María
A2 Rolfsen, Dale
AB 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.
PB Springe
SN 978-3-540-15680-2
YR 1985
FD 1985
LK https://hdl.handle.net/20.500.14352/65468
UL https://hdl.handle.net/20.500.14352/65468
NO Proceedings of a Conference held in Vancouver, Canada, June 2–4, 1983
DS Docta Complutense
RD 5 abr 2025