This paper studies the moduli space of solutions to the Bogomolny equation on R^3 with a certain type of knot singularity. For technical reasons, I have to assume the monodromy along the meridian of the knot lies in (0, 1/8) or in (3/8, 1/2) and I dont know how to resolve this constraint. The main result of this paper is: a neighbourhood of a solution to the Bogomolny equations on R^3 with such knot singularity in the moduli space has an analytical structure. Moreover, certain solutions (that come from gluing a model solution with the knot singularity and classical regular solutions) have a neighbourhood in the moduli space that has a manifold structure.
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