Deformation of singular connections I: G2-instantons with point singularities

We establish a multiplicative Fredholm theory for a Dirac-type operator associated to a connection with point singularities. There are two applications. 1: over a closed 7-manifold, we develop a deformation theory for G2-instantons with isolated (point) singularities. 2: for any G2−structure defined near the origin in R7, and any Hermitian Yang-Mills connection AO on S6, we show that there exists a locally defined G2-monopole asymptotic to AO at the origin.