Donaldson theory

Summary

Donaldson theory studies smooth 4-manifolds through moduli spaces of anti-self-dual connections, also called instantons, on principal $SU(2)$-bundles over them. It was started by Simon Donaldson in the early 1980s. Its first result, Donaldson's theorem, restricts the intersection forms of smooth $4$-manifolds. Its invariants, the Donaldson polynomial invariants, distinguish smooth structures on manifolds that are homeomorphic.