Knotted surfaces in 4-manifolds
Our speaker this week is Maggie Miller.
Title: Knotted surfaces in 4-manifolds
Abstract: In this talk, I will describe some interesting results and open questions in the study of surfaces smoothly knotted in 4-manifolds. Surfaces can be used in many ways to understand 4-manifolds, e.g. can be used to construct different smooth structures, to describe cobordisms, or to prove that two 4-manifolds are not equivalent. You can think of a surface in a 4-manifold as a 1-dimension up analogue of a knot in a 3-manifold, but in many ways surfaces exhibit much stranger behavior than knots – and many fundamental questions about surfaces (which we understand very well for knots) remain wide open.