A link is a smoothly embedded closed 1-dimensional submanifold in the 3-dimensional sphere S^3. In this talk we study a particular class of links, known as RBG links, and present some results arising from this framework in low-dimensional topology,  the study of smooth manifolds of  dimension 4 or less.

 

We will see how RBG links can be used to construct pairs of knots sharing a specific topological feature, that is having orientation preserving diffeomorphic traces. As notable applications of this framework, we will see that the Conway knot is not smoothly slice and has a friend for every integer slope.