= Uhlenbeck-Donaldson compactness for charge-one ASD connections
{c}
On a closed oriented Riemannian four-manifold, a sequence of $SU(2)$ <anti-self-dual connections> of second Chern number one has, modulo gauge and subsequence, either smooth convergence with charge one or smooth convergence away from one point to a flat charge-zero connection. In the second case the curvature-energy measures converge to $8\pi^2\delta_x$. Small-energy gauges give convergence away from finitely many points; removable singularities extend the limit; Chern-Simons clutching integers quantize each positive defect. Total charge one leaves only the two stated cases. A flat limit need not have trivial holonomy on a nonsimply connected base.
// Destination: geometry-and-topology.bigb
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