Geometric decompositions, algebraic models and rigidity theorems (Q805001)

Let X be a 1-connected space. Denote by h: \(\pi\) \({}_*(\Omega X)\otimes {\mathbb{Q}}\to H_{*+1}(X;{\mathbb{Q}})\) the rational Hurewicz homomorphism. X is spherically (resp. cospherically) generated if the image of h coincides with the set of primitive elements (resp. if ker h\(=[\pi_*(\Omega X)\otimes {\mathbb{Q}},\pi_*(\Omega X)\otimes {\mathbb{Q}}])\). X is said to be intrinsically spherically (resp. cospherically) generated if all the spaces with the same rational cohomology algebra (resp. with the same homotopy Lie algebra) are spherically (resp. cospherically) generated. In this paper the authors give obstructions in terms of Harrison cohomology (resp. Lie algebra cohomology) for all skeleta of X to be intrinsically spherically (resp. cospherically) generated.