PSL$(2; \mathbb{C})$ connections on 3-manifolds with $L^2$ bounds on curvature

Karen Uhlenbeck’s compactness theorem for sequences of connections with $L^2$ bounds on curvature applies only to connections on principal bundles with compact structure group. This article states and proves an extension of Uhlenbeck’s theorem that describes sequences of connections on principal PSL$(2; \mathbb{C})$ bundles over compact three-dimensional manifolds.

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Published 6 February 2014