Central Adams operators (Q1099435)

``From the introduction: ``Let X be a (pointed) finite complex with trivial rational homology. Then, for some, potentially large, integer \(s>0\) there exists a stable map \(B: \Sigma\) \({}^ sX\to X\) which induces an isomorphism \(B^*: KO^*(X)\to KO^*(\Sigma^ sX)\) in (reduced) periodic real K-theory. Such maps were first considered by Adams and Toda. Recent work of Devinatz, Hopkins and Smith shows, as a special first case of a much more general theorem, that B can be chosen to be central in the graded ring \(\pi^*_ s\{X;X\}\) of stable self-maps of X. In this note we reprove this using the elementary methods, based on a solution of the Adams conjecture, that we described in Topology 24, 475- 486 (1985; Zbl 0581.55008). The key idea comes from \textit{M. Hopkins} [Lectures at the Durham Sympos. on Homotopy Theory (1985)].''