Abstract

We prove several removable singularity theorems for singular Yang–Mills connections on bundles over Riemannian manifolds of dimensions greater than four. We obtain the local and global removability of singularities for Yang–Mills connections with L^∞ or L bounds on their curvature tensors, with weaker assumptions in the L^∞ case and stronger assumptions in the L case. With the global gauge construction methods we developed, we also obtain a ‘stability’ result which asserts that the existence of a connection with uniformly small curvature tensor implies that the underlying bundle must be isomorphic to a flat bundle.

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