Khovanov homology and the search for exotic 4-spheres

Abstract: A well-known strategy to disprove the smooth 4D Poincare conjecture is to find a knot that bounds a disk in a homotopy 4-ball but not in the standard 4-ball. Freedman, Gompf, Morrison and Walker suggested that Rasmussen’s invariant from Khovanov homology could be useful for this purpose. I will describe three recent results about this strategy: that it fails for Gluck twists (joint work with Marengon, Sarkar and Willis); that an analogue works for other 4-manifolds (joint work with Marengon and Piccirillo); and that 0-surgery homeomorphisms provide a large class of potential examples (joint work with Piccirillo).

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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