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Non-simple universal knots

  • H. M. Hilden (a1), M. T. Lozano (a2) and J. M. Montesinos (a3)
Abstract

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].

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[1] H. M. Hilden , M. T. Lozano and J. M. Montesinos . Universal knots. Knot Theory and Manifolds, Lecture Notes in Mathematics 1144 (Springer Verlag, 1985), 2559.

[1] H. M. Hilden , M. T. Lozano and J. M. Montesinos . Universal knots. Knot Theory and Manifolds, Lecture Notes in Mathematics 1144 (Springer Verlag, 1985), 2559.

[3] H. M. Hilden , M. T. Lozano and J. M. Montesinos . On knots that are universal. Topology 24 (1985), 499504.

[3] H. M. Hilden , M. T. Lozano and J. M. Montesinos . On knots that are universal. Topology 24 (1985), 499504.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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