Existence of Lefschetz fibrations on Stein and Weinstein domains

TL;DR

This paper proves that all Stein and Weinstein domains can be represented as Lefschetz fibrations over the disk, utilizing Donaldson's transversality methods.

Contribution

It establishes a universal presentation of Stein and Weinstein domains as Lefschetz fibrations, expanding the understanding of their geometric structures.

Findings

Every Stein domain admits a Lefschetz fibration structure.

Every Weinstein domain admits a Lefschetz fibration structure.

The proof uses Donaldson's quantitative transversality techniques.

Abstract

We show that every Stein or Weinstein domain may be presented (up to deformation) as a Lefschetz fibration over the disk. The proof is an application of Donaldson's quantitative transversality techniques.