Communications in Analysis and Geometry
Volume 15 (2007)
Coassociative 4-folds with conical singularities
Pages: 891 – 946
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.