 In his paper with Jones, he studied the topology of the moduli space of SU(2) instantons over a 4-sphere.They showed that the natural map from this moduli space to the space of all connections induces epimorphisms of homology groups in a certain range of dimensions, and suggested that it might induce isomorphisms of homology groups in the same range of dimensions.This became known as the Atiyah–Jones conjecture, and was later proved by several mathematicians.