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DIARMUID CROWLEY (MPI Bonn): The extended Eells-Kuiper invariant and G_2-topology (13/05/2014)


In this talk, I present joint work with Johannes Nordström where we define an extension of the classical Eells-Kuiper invariant to all closed spin 7-manifolds. With this invariant we give the classification of smooth 2-connected 7-manifolds.

I will then discuss recent developments in G_2-topology which motivated the definition of the extended Eells-Kuiper invariant, and how the extended Eells-Kuiper invariant relates the problem of counting the number of (topological) G_2-structures on a spin 7-manifold up to homotopy and spin diffeomorphism.

The talk will also serve as background for talks on G_2-manifolds by Nordström (MPI May 19th) and Goette (MI May 20th) in the following week.

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