Gerbes on G2 manifolds

On a projective complex manifold, the Abelian group of divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a G2-manifold we use coassociative submanifolds to define an analogue of the divisors, and a gauge theoretical equation for a connection on a gerbe to define an analogue of the Picard group. Then, we construct a map from the former to the later. We also prove that the canonical map from our analogue of the Picard group to the third cohomology group with integer coefficients is surjective. As a side remark we make an observation relating the topological type of coassociative submanifolds and the cohomology classes they represent.