Coassociative 4-folds with conical singularities

Abstract

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 G2 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 G2 structure, we prove a generic smoothness result for the second and third moduli spaces.