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The rational homotopy type of (n−1)‐connected manifolds of dimension up to 5n−3
Journal of Topology  (IF1.582),  Pub Date : 2020-03-18, DOI: 10.1112/topo.12133
Diarmuid Crowley, Johannes Nordström

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 ) 4 determined by the algebra H ( X ) . We then prove that if M is a closed ( n 1 ) ‐connected manifold of dimension at most 5 n 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.