# 4-manifolds with boundary and fundamental group Z

## Location

In this talk I will discuss work in progress in which we classify topological 4-manifolds with boundary and fundamental group **Z**, under some mild assumptions on the boundary. We apply this classification to provide an algebraic classification of surfaces in simply-connected 4-manifolds with S^3 boundary, where the fundamental group on the surface complement is **Z**. We also compare these homeomorphism classifications with the smooth setting, showing for example that every Hermitian form over **Z**[t^{\pm 1}] arises as the equivariant intersection form of a pair of exotic smooth 4-manifolds with boundary and fundamental group **Z**. This work is joint with Anthony Conway and Mark Powell.

**Note that the location of this seminar is different than usual.**