In this talk, the fourth in the series on Arnol'd's dream, I will show that to every 3-component link in the 3-sphere one can associate a map from the 3-torus to the 2-sphere such that the homotopy invariants of the map are essentially the link-homotopy invariants of the link. In particular, the second-order homotopy invariant of the map, which is a sort of ambiguous Hopf invariant, is exactly twice the triple linking number.