The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3

摘要

We define the Bianchi-Massey tensor of a topological space X to be a linear map B -> H*(X), where B is a subquotient of H*(X)circle times 4 determined by the algebra H*(X). We then prove that if M is a closed (n-1)-connected manifold of dimension at most 5n-3 (and n > 2) then its rational homotopy type is determined by its cohomology algebra and Bianchi-Massey tensor, and that M is formal if and only if the Bianchi-Massey tensor vanishes.