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Title:
SO(4)-structures on 7-manifolds
Speaker:
Abstract:
I will talk about the geometry of SO(4)-structures on 7-manifolds, under the restriction that the SO(4)-structure induces a metric with holonomy contained in G_2. This amounts to a condition on the torsion of the SO(4)-structure and I will describe what happens in various cases where the torsion is restricted further. Part of this description gives a characterisation of the Bryant-Salamon examples as the unique examples with torsion lying in particular subspaces. If a G_2-manifold is foliated by associative or coassociative submanifolds, then it carries a naturally defined SO(4)-structure. I will give an interpretation of a result of Baraglia about ‘semi-flat’ coassociative fibrations in this language, and talk about the case of ‘semi-flat’ associative fibrations.
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