The Whitehead link, the Borromean rings and the knot \(9_{46}\) are universal (Q760047)

It is known that every closed orientable 3-manifold is obtained as an (irregular) 3-fold branched covering of some knot in \(S^ 3\). Recently, W. Thurston proved that there is a link L in \(S^ 3\) such that every closed orientable 3-manifold is some branched covering of L. Such a link L is called a universal link. The authors prove the theorem that is the title of this paper. These universal links are much simpler than Thurston's link. (Later the same authors prove that the figure-eight knot is universal which confirms Thurston's conjecture.) The proof of the theorem is geometric but ingenious.