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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.