Donaldson theory

Donaldson theory is the study of smooth 4-manifolds using instantons. It was started by Simon Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold.

Most of the results of Donaldson theory depend on the manifold having a differential structure, and are false for topological 4-manifolds.

Many of the theorems in Donaldson theory can now be proved more easily using Seiberg–Witten theory.

See also

• Kronheimer–Mrowka basic class

References

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