Link maps in arbitrary manifolds and their homotopy invariants

In this paper we generalize Milnor's mu-invariants of classical links to certain ("kappa-Brunnian") higher dimensional link maps into fairly arbitrary manifolds. Our approach involves the homotopy theory of configuration spaces and of wedges of spheres. We discuss the strength of these invariants and their compatibilities e.g. with (Hilton decompositions of) linking coefficients. Our results suggest, in particular, a conjecture about possible new link homotopies.