On the Theory of Stein Manifolds

TL;DR

This paper explores the structure of Stein manifolds, generalizing domains of holomorphy, and investigates their key properties, equivalences, and symplectic topology development.

Contribution

It extends the concept of domains of holomorphy to Stein manifolds and analyzes their symplectic structures and properties.

Findings

Stein manifolds share key properties with domains of holomorphy

An equivalence similar to pseudoconvexity is established for Stein manifolds

The symplectic topology of Stein manifolds is developed and analyzed

Abstract

This paper examines the broad structure on Stein manifolds and how it generalizes the notion of a domain of holomorphy in $\mathbb C^n$. Along with this generalization, we see that Stein manifolds share key properties from domains of holomorphy, and we prove one of these major consequences. In particular, we investigate an equivalence, similar to domains of holomorphy and pseudoconvexity, on the class of manifolds. Then, we examine the canonical symplectic structure of Stein manifolds inherited from this equivalence, and how its symplectic topology develops.