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Diarmuid Crowley (Aberdeen): Manifolds which are like the Associative Grassmannian (19/04/2016)


The Associative Grassmannian is the 8-dimensional homogeneous space G_2/SO(4), where G_2 is the exceptional Lie Group of rank 14.

I will discuss motivations for classifying manifolds which are like the Associative Grassmannian and out line a proof of the following:

Theorem: There are precisely two diffeomorphism classes of manifolds with the cohomology ring, signature and A-hat genus of the Associative Grassmannian. Moreover these diffeomorphism classes differ by connected sum with the exotic 8-sphere.

The proof requires combining a variety of methods, perspectives and results. These are modified surgery, classical surgery, Haefliger's classification of embeddings, and results of Kruggel on the homotopy classification of certain 7-manifolds.

This talk is part of joint work with Achim Krause, Matthias Kreck and Dietmar Salamon.

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