Link Homotopy in S^n x R^{m-n} and Higher Order mu-invariants

Abstract

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.