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.
bounds on
their curvature tensors, with weaker assumptions in the 
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.