The trefoil knot is as universal as it can be

AbstractLet τp,q⊂S3 denote the p,q-torus knot. It is known that if ϕ:M→S3 is a branched covering branched along τp,q, then M is an orientable Seifert manifold with orientable base and non-zero Euler number. We prove a converse of this fact: If M is an orientable Seifert manifold with orientable base and non-zero Euler number, M is a branched covering of S3 with branching along the knot τp,q for any p,q, (p,q)=1, and 2⩽p