Cyclic and cocyclic maps and generalized Whitehead products

Abstract

Given co-H-spaces $X$ and $Y$, B. Gray has defined a co-H-space $X\circ Y$ and a natural transformation
$X\circ Y\to X\vee Y$ which leads to a generalized Whitehead product. We make use of that product and sketch ideas on its dual to examine cyclic and cocyclic maps. Given spaces $X$ and $Y$, some results on Gottlieb sets $\mathcal{G}(X,Y)$ and dual Gottlieb sets $\mathcal{DG}(X,Y)$ are stated.