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Non-simple universal knots

Published online by Cambridge University Press:  24 October 2008

H. M. Hilden ,
M. T. Lozano  and
J. M. Montesinos
H. M. Hilden
Affiliation:
University of Hawaii, U.S.A.
M. T. Lozano
Affiliation:
Universidad de Zaragoza, Spain
J. M. Montesinos
Affiliation:
Universidad Complutense de Madrid, Spain
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Extract

A link or knot in S3 is universal if it serves as common branching set for all closed, oriented 3-manifolds. A knot is simple if its exterior space is simple, i.e. any incompressible torus or annulus is parallel to the boundary. No iterated torus knot or link is universal, but we know of many knots and links that are universal. Thurston gave the first examples of universal links [8], and subsequently we proved that all 2-bridge knots and links that can be universal (no torus knots or links) are in fact universal [3]. Some other universal knots are described in [1] and [2], together with a general procedure for constructing such knots. For a general reference to knots see [9].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 87 - 95
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

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