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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

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