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

TL;DR

This paper extends Uhlenbeck's compactness theorem to include sequences of PSL(2;C) connections on 3-manifolds with L2 curvature bounds, broadening the scope of gauge theory analysis.

Contribution

It provides a new compactness result for PSL(2;C) connections on 3-manifolds, which was not covered by previous theorems for compact structure groups.

Findings

Extended Uhlenbeck's theorem to PSL(2;C) connections

Established compactness for sequences with L2 curvature bounds

Applicable to gauge theory on 3-manifolds

Abstract

Karen Uhlenbeck's compactness theorem for sequences of connections with L2 bounds on curvature applies only to connections on principal bundles with compact structure group. This article states and proves an extension of Uhlenbecks theorem that describes sequences of connections on principal PSL(2;C) bundles over compact three dimensional manifolds.