Cohomology in algebra, geometry, physicsand statistics

The rational homotopy type of k-connected manifolds of dimension < 5k+3

The main aim of the talk is to introduce the "Bianchi-Massey tensor" of a topological space: a certain linear map on a subspace of the fourth tensor power of the rational cohomology, with symmetries analogous to the Riemann curvature tensor. In the case of closed k-connected manifolds of dimension at most 5k+2 (with k > 0), the cohomology algebra and Bianchi-Massey tensor turn out to be enough to completely determine the rational homotopy type, i.e., the equivalence class up to continuous maps that induce isomorphisms on the rationalised homotopy groups. This is joint work with Diarmuid Crowley.