  We study the stability of coassociative 4-folds with conical singularities
under perturbations of the ambient G_2 structure by defining an integer
invariant of a coassociative cone which we call the stability index. The
stability index of a coassociative cone is determined by the spectrum of the
curl operator acting on its link. We explicitly calculate the stability index
for cones on group orbits. We also describe the stability index for cones
fibered by 2-planes over algebraic curves using the degree and genus of the
curve and the spectrum of the Laplacian on the link. Finally we apply our
results to construct the first known examples of coassociative 4-folds with
conical singularities in compact manifolds with G_2 holonomy.
