Link concordance invariants and homotopy theory

Abstract

We show that each of a sequence of concordance invariants for codimension-two links of spheres inS n+2 , defined by Kent Orr, is identically zero forn>1. For classical links (n=1), the same proof shows that these invariants vanish if and only if Milnor's $$\bar \mu $$ vanish (a result obtained independently and earlier by Orr himself). We offer sufficient conditions for the vanishing of Orr's ω-invariant (not covered by the above). We discuss how this relates to positive results.