Ciprian Manolescu – Stanford University
Khovanov Homology and Four-Dimensional Topology
11 May 2023 Thursday, 12:00 (New York), 17:00 (Londra), 19:00 (Istanbul)
Over the last forty years, most progress in four-dimensional topology came from gauge theory and related invariants. Khovanov homology is an invariant of knots in R^3 of a different kind: its construction is combinatorial, and connected to ideas from representation theory. There is hope that it can tell us more about smooth 4-manifolds; for example, Freedman, Gompf, Morrison and Walker suggested a strategy to disprove the 4D Poincare conjecture using Rasmussen’s invariant from Khovanov homology. It is yet unclear whether their strategy can work. I will explain a new attempt to pursue it (joint work with Lisa Piccirillo) and some of the challenges we encountered. I will also review other topological applications of Khovanov homology.
YouTube Recording of the Talk