A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking

We construct the hyper-Kähler moduli space of framed monopoles over ${\mathbb{R}}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.