Stein domains and the Oka-Grauert principle

Geometry Topology Working Seminar
Friday, September 14, 2018 - 1:55pm
1.5 hours (actually 80 minutes)
Skiles 006
Georgia Insitute of Technology
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.