Coassociative 4-folds with conical singularities

This article studies the deformation theory of coassociative 4-folds $N$ with conical singularites in a $G_2$ manifold. We describe three moduli spaces: first we consider deformations with the same singularities as $N$, then allow for changes in the singularities and, finally, include variations of the ambient $H_2$ structure. We show that the moduli space, in each case, is locally homeomorphic to the kernel of a smooth map between smooth manifolds and determine a lower bound for its expected dimension. Further, by relaxing the condition on the $G_2$ structure, we prove a generic smoothness result for the second and third moduli spaces.

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Published 1 January 2007