k-component link defines a map
T^k --> Conf_k S^3. Does the homotopy type of this map capture the Milnor invariants?
Some special cases:
k=2, no, it's null homologous, but you can look instead at the map
T^2 --> Conf_2 R^3, which captures linking number.
k=3, Melvin et al. proved it does.