Universal knots

Abstract

In an unpublished preprint W. Thurston showed the existence of a six component link in the 3-sphere such that every three-manifold can be expressed as a branched cover of the 3-sphere branched over this link. He called links with this property "universal links'' and asked if a universal knot exists. The authors confirm this by showing that any link can be embedded in the branch locus of a 3-sphere branched covering of a 3-sphere branched over a knot