Classification of broken Lefschetz fibrations with small fiber genera

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 up to blow-ups.