Cohomologie de Harrison et espaces projectifs tronques (Q1072158)

One finds here a careful rational homotopy analysis of truncated projective spaces \({\mathbb{C}}P^{\infty}/{\mathbb{C}}P^ n\). Main results: explicit determination of the minimal model and of the rational homotopy Lie algebra; \({\mathbb{C}}P^{\infty}/{\mathbb{C}}P^ n\) is not coformal but there is only one more Q-type within its rational homotopy Lie algebra, namely the coformal one. On the other hand the truncated projective spaces offer intrinsic formal examples with non-bounded cohomology whose defining relations are not given by regular sequences. Establishing their intrinsic formality is rather delicate and is based on the interpretation of the Halperin-Stasheff obstructions to formality [\textit{S. Halperin} and \textit{J. Stasheff}, Adv. Math. 32, 233-279 (1979; Zbl 0408.55009)] as Harrison cohomology classes [cf. previous work of the author, Lect. Notes Math. 1183, 361-370 (1986)].