Abstract:
Generalising work of Freedman-Quinn and Stong from 30-40 years ago, we prove a surface embedding theorem for 4-manifolds with good fundamental group, in the presence of potentially unframed dual spheres. The essential obstruction is the Kervaire-Milnor invariant, and I will describe how to compute it and present some useful corollaries of the theorem. The goal of the talk is to be reasonably self-contained, and no prior expert knowledge of 4-manifold topology should be required. This is joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.