Stein structures: existence and flexibility

TL;DR

This survey reviews the topology of Stein manifolds, focusing on their existence and flexibility properties, based on lectures and recent research developments.

Contribution

It compiles and synthesizes recent advances in understanding Stein structures, highlighting their existence criteria and flexibility features.

Findings

Summarizes key topological properties of Stein manifolds

Highlights recent progress in Stein structure flexibility

Provides a comprehensive overview from recent lectures

Abstract

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.