Abstract
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 G 2 -instantons with isolated (point) singularities. 2: for any G 2 − structure defined near the origin in R 7 , and any Hermitian Yang–Mills connection A O on S 6 , we show that there exists a locally defined G 2 -monopole asymptotic to A O at the origin.
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