Trisections of 4-manifolds via Lefschetz fibrations

Nickolas A. Castro, Burak Ozbagci

Published 2017-05-27Version 1

We use Lefschetz fibrations to give an alternate proof of a recent result of Gay and Kirby which says that every smooth, closed, oriented, connected 4-manifold admits a trisection. The key feature of our proof is that contact geometry plays a crucial role instead of Cerf theory. As an application, we describe an explicit trisection diagram of a closed 4-manifold which admits a Lefschetz fibration over the 2-sphere equipped with a section of square -1, based only on the vanishing cycles of the Lefschetz fibration.