The existence of a transverse universal knot

Abstract

We prove that there is a knot K transverse to ξ std , the tight contact structure of S 3 , such that every contact 3-manifold (M, ξ) can be obtained as a contact covering branched along K. By contact covering we mean a map ϕ : M → S 3 branched along K such that ξ is contact isotopic to the lifting of ξ std under ϕ.