The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two Dehn surgeries with different surgery coefficients r and r' results in distinct oriented three-manifolds. Earlier works on the conjecture imply that one needs to consider only the case r'=-r and r=2 or 1/n for some integer n. In this talk, I'll explain how one can remove the case of r=1/n, reducing the conjecture to the case r=2. Furthermore, in the case r=2, the Alexander polynomial of the knot is trivial. The key tools in the proof are a persistence module associated to any integer homology sphere using instanton gauge theory and an exact triangle relating instanton Floer homology groups of 1/n-surgeries on a knot. This talk is based on a joint work with Tye Lidman and Mike Miller Eismeier.

Online via Zoom:
Meeting ID: 908 611 6889
Passcode: 362880