Can Embedding Problems Be Used to Distinguish S^4 from Other Homotopy 4-Spheres?

Explore a mathematical lecture examining potential methods for distinguishing S^4 from other homotopy 4-spheres through embedding problems. Delve into alternative approaches beyond traditional Khovanov homology methods, focusing on the transition from surfaces to 3-manifolds and their embedding properties. Learn about the unique conditions imposed on Heegaard diagrams when embedding closed 3-manifolds in S^4, and discover potential applications of these constraints. Gain insights from Harvard CMSA's Michael Freedman as he investigates this fundamental question in topology and discusses possible strategies for exploiting these mathematical relationships.