Oka-Grauert principle
= Oka-Grauert principle
{c}
For a complex Lie group, holomorphic <principal bundles> over a <Stein manifold> are classified up to holomorphic isomorphism by their topological bundle class. In particular, a topologically trivial holomorphic <principal bundle> over a Stein base has a global holomorphic trivialization. This supplies global complex gauges for a flat partial connection on contractible complex affine space; it does not impose prescribed behaviour at infinity.