Coassociative K3 Fibrations of Compact G2-manifolds
نویسندگان
چکیده
A class of examples of Riemannian metrics with holonomy G2 on compact 7-manifolds was constructed by the author in [Ko] using a certain ‘generalized connected sum’ of two asymptotically cylindrical manifolds with holonomy SU(3). We consider, on each of the two initial SU(3)-manifolds, a fibration arising from a Lefschetz pencil of K3 surfaces. The gluing of the two K3 fibrations yields a coassociative fibration of the connected sum G2-manifold over a 3-dimensional sphere. The singular fibres of this fibration are diffeomorphic to K3 orbifolds with ordinary double points and are parameterized by a Hopf-type link. We believe that these are the first examples of fibrations of compact manifolds of holonomy G2 by coassociative minimal submanifolds.
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