Seminar| Institute of Mathematical Sciences
Time: Thursday, November 5th, 2026,15:30-16:30
Location: IMS S408
Speaker: Xingpei Liu, Peking University
Abstract: The (Dehn) surgery number of a closed oriented 3-manifold Y is the minimum number of components of a framed link L in S^3 such that Y is obtained by surgery on L. In this talk, I will explain how instanton Floer homology with mod 2 coefficients provides new lower bounds for surgery number. The key ingredients include a cobordism inequality for Frøyshov's invariant q3, which applies even to cobordisms with indefinite intersection forms. As applications, we determine the surgery numbers of connected sums of copies of the Poincaré homology sphere and construct hyperbolic integer homology spheres with arbitrarily large surgery numbers, answering a question of Auckly. This is joint work with Aliakbar Daemi and Mike Miller Eismeier.