Geometry of broken Lefschetz fibrations
Speaker: Ramon Vera, Penn State
Abstract: In this talk, we will discuss two geometric structures that are naturally associated to broken Lefschetz fibrations: near-symplectic forms and singular Poisson structures. Broken Lefschetz fibrations, or bLfs, were introduced by Auroux, Donaldson, and Katzarkov as mappings from a 4-manifold to the 2-sphere with two types of singularities. The natural geometric structure of these mappings is a near-symplectic form. This connects to an idea of Taubes of studying near-symplectic structures on 4-manifolds as a generalization of symplectic topology. Since then, these fibrations have found applications in low-dimensional topology and symplectic geometry. One reason is that every 4-manifold admits a bLf. After introducing bLfs, we will describe near-symplectic forms and present the generalization in higher dimensions. Using bLfs, we will also see a link to Poisson geometry. Any homotopy class of maps from a 4-manifold to the 2-sphere admits a singular Poisson structure of rank 2, whose foliation is compatible with the fibres of a bLf.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm