Sur le type d'homotopie d'un CW-complexe (Q1397810)

The paper under review (essentially the author's PhD thesis) deals with homotopy classification of simply connected \(CW\)-complexes. For this purpose, the author introduces the concept of a \(\Gamma\)-system, which encodes \textit{J. H. C. Whitehead}'s exact sequence [Ann. Math. (2) 52, 51--110 (1950; Zbl 0037.26101)] together with additional algebraic structure, necessary to reconstruct the homotopy type of a simply connected \(CW\)-complex out of its \(\Gamma\)-system. The author relies here on ideas of \textit{H. J. Baues} [Homotopy type and homology. Oxford Mathematical Monographs (1996; Zbl 0857.55001)]. The main theorem states that two simply connected \(CW\)-complexes are homotopy equivalent if and only if their \(\Gamma\)-systems are equivalent.