Yang–Mills instantons have been explicitly constructed in many cases by means of twistor theory, which relates them to algebraic vector bundles on algebraic surfaces, and via the ADHM construction, or hyperkähler reduction (see hyperkähler manifold), a geometric invariant theory procedure. The groundbreaking work of Simon Donaldson, for which he was later awarded the Fields medal, used the moduli space of instantons over a given four-dimensional differentiable manifold as a new invariant of the manifold that depends on its differentiable structure and applied it to the construction of homeomorphic but not diffeomorphic four-manifolds. Many methods developed in studying instantons have also been applied to monopoles. This is because magnetic monopoles arise as solutions of a dimensional reduction of the Yang–Mills equations.