  Given a suitable link map f into a manifold M, we constructed, in [10], link
homotopy invariants kappa(f) and mu(f). In the present paper we study the case
M=S^n x R^{m - n} in detail. Here mu(f) turns out to be the starting term of a
whole sequence mu^(s)(f), s = 0, 1, ..., of higher mu-invariants which together
capture all the information contained in kappa(f). We discuss the geometric
significance of these new invariants. In several instances we obtain complete
classification results. A central ingredient of our approach is the homotopy
theory of wedges of spheres.

Algebraic Topology;Geometric Topology