Martin Kerin

On the classification of a certain family of non-negatively curved 7-manifolds

A 2-connected, rational homotopy 7-sphere is classified up to diffeomorphism by three invariants: its (finite) 4^th cohomology group, its q-invariant and its Eells–Kuiper invariant. The q-invariant is a quadratic refinement of the linking form and determines the homeomorphism type, while the Eells–Kuiper invariant then pins down the diffeomorphism type. In this talk, I will discuss the homeomorphism and diffeomorphism classifications of a certain family of non-negatively curved, 2-connected, rational homotopy 7-spheres, discovered by Sebastian Goette, Krishnan Shankar and myself. This family contains, in particular, all S³-bundles over S⁴ and all exotic 7-spheres.