LINK HOMOTOPY IN Sn×ℝm-n AND HIGHER ORDER μ-INVARIANTS

Abstract

Given a suitable link map f into a manifold M, we constructed, in a previous publication, link homotopy invariants κ(f) and μ(f). In the present paper we study the case M=Sn×ℝm-n in detail. Here μ(f) turns out to be the starting term of a whole sequence μ(s)(f), s=0, 1,…, of higher μ-invariants which together capture all the information contained in κ(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.