Classification of broken Lefschetz fibrations with small fiber genera

TL;DR

This paper extends the classification of genus one Lefschetz fibrations to include simplified broken Lefschetz fibrations with fibers of genus one and zero, using chart descriptions to identify the 4-manifolds that admit such fibrations.

Contribution

It introduces a classification framework for genus one simplified broken Lefschetz fibrations, expanding the understanding of 4-manifolds with these structures.

Findings

Classified genus one Lefschetz fibrations over the 2-disk with specific monodromies.

Identified 4-manifolds admitting genus one simplified broken Lefschetz fibrations.

Abstract

In this article, we generalize the classification of genus one Lefschetz fibrations to genus one simplified broken Lefschetz fibrations, which have fibers of genera one and zero. We classify genus one Lefschetz fibrations over the 2-disk with certain non-trivial global monodromies using chart descriptions, and identify the 4-manifolds admitting genus one simplified broken Lefschetz fibrations.