Taubes' method on the study of the Bogomolny equations on R^3

Abstract: Suppose A is an SU(2) connection R^3 whose curvature is F. Suppose Φ is a section over the adjoint bundle of the SU(2) bundle. Then the Bogomolny equations is written as F = *d_A Φ, there * is the Hodge-star operator.

The Bogomolny equations has been widely studied using different methods. One of them is Taubes' analytical method in 1980s, which can be used to prove that the moduli space of the Bogomolny equations with certain assymptotic conditions (up to SU(2) gauge transformations) has a manifold structure. In this talk, I will mainly introduce Taubes' method on studying the Bogomolny equations. I will also talk about how Taubes' method may be adapted to study the Bogomolny equations on R^3 with a knot singularity.