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

Citations:

Zbl 0037.26101; Zbl 0857.55001
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