Donaldson [J. Differential Geom. 53 (1999) 205–236] showed that every closed symplectic –manifold can be given the structure of a topological Lefschetz pencil. Gay and Kirby [Geom. Topol. 20 (2016) 3097–3132] showed that every closed –manifold has a trisection. In this paper we relate these two structure theorems, showing how to construct a trisection directly from a topological Lefschetz pencil. This trisection is such that each of the three sectors is a regular neighborhood of a regular fiber of the pencil. This is a –dimensional analog of the following trivial –dimensional result: for every open book decomposition of a –manifold , there is a decomposition of into three handlebodies, each of which is a regular neighborhood of a page.
"Trisections of Lefschetz pencils." Algebr. Geom. Topol. 16 (6) 3523 - 3531, 2016. https://doi.org/10.2140/agt.2016.16.3523