Hello everyone,

Seminar is today in 405. 

Nick Castro from UArk is speaking his title and abstract are below:

Lefschetz Fibrations and Relative Trisections 

Speaker: Nickolas Castro, University of Arkansas 

Date: Oct 9, 2018 

Time: 2:30 PM 

Room: MSCS 405 

Abstract: A relative trisection of a smooth 4-manifold with boundary is a decomposition into three diffeomorphic, codimension zero subspaces whose pairwise intersections are 3-dimensional cobordisms, and triple intersection is a surface with boundary. Such a decomposition can be uniquely described by a collection of curves on this surface, called a relative trisection diagram. From this diagram, we can algorithmically determine the structure induced on the bounding 3-manifold(s), called an open book decomposition. A Lefschetz fibration on a smooth 4-manifold is a map which is locally a surface bundle away from its isolated critical points. Lefschetz fibrations can also be described by curves on a surface and, in the case of manifolds with boundary, also induce an open book decomposition on the boundary. In this talk, I will define these structures and discuss how to obtain a trisection from a Lefschetz fibration. I will present an alternate proof on the existence of trisection of closed 4-manifolds by way of Lefschetz fibrations and the gluing theorem. Finally, I will discuss the uniqueness of relative trisections which induce different open book decompositions.