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Sur le type d’homotopie d’un CW-complexe. (French) Zbl 1041.55004

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 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 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.

MSC:

55P15 Classification of homotopy type
55U15 Chain complexes in algebraic topology
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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