Broken Lefschetz fibrations and Floer theoretical invariants

Geometry Topology Seminar
Monday, December 1, 2008 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 269
Yanki Lekili – MIT
John Etnyre
A broken fibration is a map from a smooth 4-manifold to S^2 with isolated Lefschetz singularities and isolated fold singularities along circles. These structures provide a new framework for studying the topology of 4-manifolds and a new way of studying Floer theoretical invariants of low dimensional manifolds. In this talk, we will first talk about topological constructions of broken Lefschetz fibrations. Then, we will describe Perutz's 4-manifold invariants associated with broken fibrations and a TQFT-like structure corresponding to these invariants. The main goal of this talk is to sketch a program for relating these invariants to Ozsváth-Szabó invariants.