Abstract
The aim of this paper is to consider the following problem: given a simply connected CW complex X of finite type, find the cardinal of the set of rational homotopy types of CW complexes Y such that H*(Y, ℚ) is isomorphic, as a commutative graded algebra, to H*(X, ℚ). For this purpose we introduce a long exact sequence, called the Whitehead exact sequence, which we associated with the minimal Sullivan model of X and which allows us to define the notion of the adapted couple associated with X. Thus we show that the rational homotopy type of X is completely determined by the equivalence class of its adapted couple.
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