Topology of generic foliations on Stein manifolds: structure of leaves and Kupka-Smale property

TL;DR

This paper investigates the topology of leaves in singular holomorphic foliations on Stein manifolds, revealing that most leaves are contractible or cylinders and that generic foliations satisfy the Kupka-Smale property.

Contribution

It establishes the typical topological structure of leaves and the Kupka-Smale property for generic foliations on Stein manifolds.

Findings

Most leaves are contractible

Remaining leaves are topological cylinders

Generic foliations are complex Kupka-Smale

Abstract

We study topology of leaves of 1-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.