An afternoon of low dimensional topology at CMSA
CMSA EVENTS
June 4, 2024 2:00-4:00 PM
Harvard CMSA 20 Garden St., Room G10
Zoom: https://harvard.zoom.us/j/977347126
Password: cmsa
2:00–3:00 pm ET
Slava Krushkal, University of Virginia
Corks for exotic diffeomorphisms
Exotic smooth structures on simply-connected 4-manifolds are known to be related by cork twists: cutting out and re-gluing certain smooth contractible submanifolds. Work in progress, joint with A. Mukherjee, M. Powell, and T. Warren, provides a localization result for exotic diffeomorphisms of 4-manifolds. I will also discuss applications to known examples of exotic diffeomorphisms.
4:00–5:00 pm ET
Michael Freedman, Harvard CMSA
Can embedding problems be used to distinguish S^4 from other (possible) homotopy 4-spheres? 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.