Homotopy classification of 3-component links of codimension greater than 2 (Q2638606)

Given an embedded link f: \(S^ p\coprod S^ q\coprod S^ r\hookrightarrow {\mathbb{R}}^ m\) with \(p,q,r<m-2\), the author discusses its \(\kappa\)-invariant and the homotopy set \([S^ p\times S^ q\times S^ r,F_ 3({\mathbb{R}}^ m)]\) in which \(\kappa\) (f) lies [cf. the reviewer, Lect. Notes Math. 1172, 116-129 (1985; Zbl 0578.58005)]. He concludes that the stabilized Haefliger-Steer invariant [\textit{A. Haefliger} and \textit{B. Steer}, Comment. Math. Helv. 39, 259-270 (1965; Zbl 0127.137)] depends on f only up to link homotopy; in an appropriate dimension range this leads to a complete link homotopy classification of such links. [Reviewer's remark: the stabilized Haefliger-Steer invariant of f is actually just the generalized Milnor invariant \(\pm \mu (f)\); this follows from a paper of the reviewer [Topology 30, No.2, 267-281 (1991)], as do further homotopy classification results even for non-embedded link maps with any number of components.]