2015/05/31 by Diarmuid Crowley, Johannes Nordström · 1 citation
Mathematics · #math.AT #math.GT #msc:55P62 #msc:57N65
paper · pdf · doi:10.1112/topo.12133
published as J. Top. 13 (2020), 539-575 · 31 pages. v3: Corrected statement of Theorem 1.5. To appear in the Journal of Topology
arxiv created 2019/10/22 · arxiv updated 2020/05/12
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.