Seminars & Colloquia Calendar
Khovanov homology and four-manifolds
Ciprian Manolecu (Stanford)
Location: zoom
Date & time: Wednesday, 10 February 2021 at 3:30PM - 4:30PM
Abstract: 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 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 smooth 4D Poincare conjecture
using Rasmussen's invariant from Khovanov homology. It is yet unclear
whether their strategy can work, and I will explain some of its
challenges. I will also review other topological applications of
Khovanov homology, with regard to smoothly embedded surfaces in
4-manifolds.
