Geometry and Topology Seminar: Cosmetic Surgery By Energy and Triangles

Abstract: The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to $\pm 2$ or $\pm 1/n$-surgeries being the only possible cosmetic surgeries. In this talk, I'll explain how one can remove the case of $\pm 1/n$-surgeries, reducing the conjecture to the case of $\pm 2$-surgery on knots with trivial Alexander polynomial. This talk is based on a joint work with Lidman and Miller Eismeier.

Host: Angel Roman