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Aspects of G2 Geometry (G2 Geometry)
Start date: Oct 1, 2010, End date: Sep 30, 2013 PROJECT  FINISHED 

"A first objective of this proposal is to construct large numbers of new G2 manifolds by extending Kovalev's ``connect sum"" construction to a larger class of 3-folds. This will be achieved via a combination of differential, algebraic and analytic methods which will lead to a very good understanding of the topology of these manifolds, of the relationship to the geometry of the generating 3-folds, and of the limits of the ``connect sum"" construction.A second objective is to construct new examples of associative submanifolds, partly using the above results, and to study moduli spaces of associative submanifolds with respect to various notions of ``tame"" G2 structures.A third objective is to construct holomorphic 3-folds with trivial canonical class starting from integral affine manifolds."
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