Abstract:
In 1982 William Thurston showed the existence of a universal link; every 3-manifold is a branched covered over the 3-sphere with branching set that link. A similar phenomenon has been found in the context of contact manifolds, but now the link is required to be a transverse link (See [1]). We are going to discuss the main ideas of the proof and all the concepts required to understand the principal result. 

[1] Casals, R., Etnyre, J.~B.\ 2017, arXiv:1712.09968 TRANSVERSE UNIVERSAL LINKS