The certain exact sequence of Whitehead and the classification of homotopy types of CW-complexes (Q989105)

Let \(X\) and \(Y\) be two simply connected CW-complexes. In this paper the author shows that any strong morphism (\(f_{*}, \gamma_{*})\) (where \(f_{*}: H_{*}(X; \mathbb{Z}) \rightarrow H_{*}(Y; \mathbb{Z})\), \(\gamma_{*}: \Gamma_{*}^{X} \rightarrow \Gamma_{*}^{Y}\)) from \textit{J.H.C. Whitehead}'s certain exact sequence, see [Ann. Math. (2) 52, 51--110 (1950; Zbl 0037.26101], gives rise to a map \(\alpha: X \rightarrow Y\) such that \(\alpha _{*} = f_{*}\).