Geometry Seminar

Seifert fibered 4-manifolds are the 4-dimensional analog of Seifert 3-manifolds in that these are the 4-manifolds which admit a fixed-point free smooth circle action. In this talk I'll first review what is known and then present some recent results about Seifert 4-manifolds. In particular, I will discuss several results which show that the smooth structure of a Seifert 4-manifold is largely determined by its underlying topological structures, such as homotopy type or homeomorphism type, which is in contrast to the well-known fact that in dimension 4, a homeomorphism type may and very often support infinitely many distinct diffeomorphism types.