"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."
Field of science
- /natural sciences/mathematics/pure mathematics/topology
- /natural sciences/mathematics/pure mathematics/geometry
Call for proposal
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