Simplified broken Lefschetz fibrations and trisections of 4-manifolds

Abstract

Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.