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  "body": "\n## Summary\n\nDonaldson theory studies smooth [[4-manifolds|8H58Q6YJCH]] through moduli spaces of anti-self-dual connections, also called [[instantons|YWBTGC7MFA]], on principal $SU(2)$-bundles over them.\nIt was started by Simon Donaldson in the early 1980s.\nIts first result, [[Donaldson's theorem|34B7K77P31]], restricts the intersection forms of smooth $4$-manifolds.\nIts invariants, the Donaldson polynomial invariants, distinguish smooth structures on manifolds that are homeomorphic.\n\n## Explanations\n\n### L1 human\n\nA connection is a rule for comparing directions at nearby points, and its curvature measures how much the rule twists.\nOn a four-dimensional space, the connections whose curvature has a special symmetry, the instantons, form a new space called a moduli space.\nThe shape of this moduli space reflects the smooth structure of the original space, not only its topology.\nFor example, it shows that the topological $4$-manifold with the $E_8$ intersection form cannot be smooth.\nThe [[Seiberg–Witten invariants|PRDDMSTR4X]] later gave a simpler route to many of the same results.\n",
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