Topology Seminar: Simplifying broken Lefschetz fibrations and trisections of 4-manifolds
Speaker: Osamu Saeki
Abstract: We present explicit algorithms for simplifying the topology of indefinite fibrations on 4-manifolds, which include broken Lefschetz fibrations and indefinite generic maps, from the viewpoint of singularity theory. These algorithms allow us to give purely topological and constructive proofs of the existence of simplified broken Lefschetz fibrations on general 4-manifolds, and a theorem of Auroux-Donaldson-Katzarkov on the existence of simplified broken Lefschetz pencils on near-symplectic 4-manifolds. We moreover establish a correspondence between broken Lefschetz fibrations and trisections of 4-manifolds, and show the existence of simplified trisections on all 4-manifolds. Based on this correspondence, we provide several examples of simplified trisections.
Friday, October 23, 2020 at 7:00pm