Csaba Nagy: Classification of certain 8-manifolds

I will consider simply-connected spin 8-manifolds with the homology of an r-fold connected sum of S^2 x S^6. The set of diffeomorphism classes of such manifolds forms a finitely generated abelian group, \Theta(r).
In this talk I will sketch a proof that \Theta(r) is isomorphic to other groups of geometric interest, specifically the mapping class group of a certain 7-manifold and also a group of framed links studied by Haefliger. I will also show how these isomorphisms can be used to compute \Theta(r).