An afternoon of low dimensional topology at CMSA


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June 4, 2024 2:00 pm - 5:00 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

June 4, 2024 2:00-4:00 PM

Harvard CMSA 20 Garden St., Room G10


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.