a1 University of Hawaii, U.S.A.
a2 Universidad de Zaragoza, Spain
a3 Universidad Complutense de Madrid, Spain
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 , and subsequently we proved that all 2-bridge knots and links that can be universal (no torus knots or links) are in fact universal . Some other universal knots are described in  and , together with a general procedure for constructing such knots. For a general reference to knots see .
(Received December 18 1985)
(Revised October 24 1986)