Georgia Institute of Technology College of Sciences

The Oka-Grauert principle is one of the first examples of an h-principle. It states that for a Stein domain X and a complex Lie group G, the topological and holomorphic classifications of principal G-bundles over X agree. In particular, a complex vector bundle over X has a holomorphic trivialization if and only if it has a continuous trivialization. In these talks, we will discuss the complex geometry of Stein domains, including various characterizations of Stein domains, the classical Theorems A and B, and the Oka-Grauert principle.