[For the entire collection see Zbl 0577.00005.]
The author states and proves a theorem in rational homotopy which is an analog of the famous unsolved problem due to J. H. C. Whitehead as to whether or not subcomplexes of aspherical two-dimensional CW complexes are aspherical. The result is: Let \(W=\bigvee_{\alpha \in I}S^{d_{\alpha}}\), where I is any indexing set and \(d_{\alpha}\geq 2\). Suppose Y is obtained by attaching cells to W, \(Y=W\cup_{f}(\cup_{\beta \in J}e^{d_{\beta}})\) for some indexing set J and dimensions \(d_{\beta}\geq 3\) and suppose X is a subcomplex of Y containing W. If \((i_{WY})_{\#}: \Pi_*(W,w_ 0)\otimes {\mathbb{Q}}\to \Pi_*(Y,w_ 0)\otimes {\mathbb{Q}}\) is surjective then \((i_{WX})_{\#}: \Pi_*(W,w_ 0)\otimes {\mathbb{Q}}\mapsto \Pi_*(X,w_ 0)\otimes {\mathbb{Q}}\) is surjective. To prove the result the author uses the Adams-Hilton model of a space and inert (or strongly free) sequences in \(H_*(\Omega W)\otimes {\mathbb{Q}}.\)