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

Abstract

We define the Bianchi-Massey tensor of a topological space X to be a linear map from a subquotient of the fourth tensor power of H*(X). We then prove that if M is a closed (n-1)-connected manifold of dimension at most 5n-3 (and n > 1) 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. We use the Bianchi-Massey tensor to show that there are many (n-1)-connected (4n-1)-manifolds that are not formal but have no non-zero Massey products, and to present a classification of simply-connected 7-manifolds up to finite ambiguity.

31 pages. v3: Corrected statement of Theorem 1.5. To appear in the Journal of Topology

References in corpus (2)

• Algebra+Homotopy=Operad
• A-infinity structures and Massey products

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