A class of examples of smooth compact manifolds of holonomy G2 was previously constructed by the author using a certain `generalized connected sum' of two asymptotically cylindrical manifolds of holonomy
SU(3) at their ends. We consider, on each of the two initial SU(3)-manifolds, a K3 fibration (with some singular fibres) arising from holomorphic geometry. Using analysis we show that the gluing of the two K3 fibrations yields a fibration of the ambient G2-manifold over the 3-dimensional sphere, with fibres coassociative minimal submanifolds. The result may be viewed, in particular, as an odd-dimensional analogue of the elliptic fibrations of K3 surfaces.
SU(3) at their ends.
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