Removable singularities for Yang-Mills connections in higher dimensions

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 Ln/2 bounds on their curvature tensors, with weaker assumptions in the L∞ case and stronger assumptions in the Ln/2 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.