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Karen Uhlenbeck's compactness theorem for sequences of connections with L2bounds on curvature applies only to connections on principal bundles withcompact structure group. This article states and proves an extension ofUhlenbecks theorem that describes sequences of connections on principalPSL(2;C) bundles over compact three dimensional manifolds.

PSL(2;C) connections on 3-manifolds with L2 bounds on curvature