Speaker: Michael Freedman, Harvard CMSA

Title: Can embedding problems be used to distinguish S^4 from other (possible) homotopy 4-spheres?

Abstract: There are approaches in the literature (using Khovanov homology) to detecting a homotopy 4-sphere, via the 4-ball genus of knots. I’d like to suggest moving from surfaces to 3-manifolds, that is approaching the problem by considering the which closed 3-manifolds embed.  Embedding in the actual S^4 implies a curious condition on the possible Heegaard diagrams for the 3-manifold. I’ll explain this condition and speculate on how it might be exploited.