A Note on Lefschetz Fibrations on Compact Stein 4-Manifolds

TL;DR

This paper provides an intrinsic alternative proof that every compact Stein surface admits a Lefschetz fibration over the 2-disk with bounded fibers, offering a new perspective on a known result.

Contribution

It introduces a more intrinsic proof of the existence of Lefschetz fibrations on compact Stein surfaces, complementing prior approaches.

Findings

Every compact Stein surface admits a Lefschetz fibration over the 2-disk.

The proof is more intrinsic compared to previous methods.

The result enhances understanding of Stein surface structures.

Abstract

Loi-Piergallini and Akbulut-Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the 2-disk with bounded fibers. In this note we give a more intrinsic alternative proof of this result.