Monday March 31st, 2025 | |
| Time: | 12:30 PM - 1:55 PM |
| Title: | ASD Connections & Cosmetic Surgery |
| Speaker: | Mike Miller Eismeier, University of Vermont |
| Location: | Math P-131 |
| Abstract: | |
| The cosmetic surgery conjecture predicts that, given a knot K in a 3-manifold, the oriented diffeomorphism type of surgery on K determines the surgery slope (up to oriented diffeomorphism). For knots in the 3-sphere, a sequence of restrictions coming from Heegaard Floer homology implies that if the cosmetic surgery is false for K, then r-surgery on K is not oriented diffeomorphic to (-r)-surgery, for some r in {2, 1, 1/2, 1/3, …}, but Heegaard Floer homology techniques reach a limit here. I will discuss how a quantitative enhancement of instanton homology rules out the cases r = 1/n, leaving only the possibility of 2-surgery. I will discuss limitations of this approach as well as possible future developments. | |