Topology Seminar- Invariants of 4-manifolds from Khovanov-Rozansky link homology

Speaker:Paul Wedrich (Max Planck Institute for Mathematics & University of Bonn)
Date and time: Tuesday, April 28, 4:00--5:00pm
Place: Online via Zoom (if you plan to participate please e-mail to J.Przytycki ([email protected])
Title:  Invariants of 4-manifolds from Khovanov-Rozansky link homology

Abstract: .Ribbon categories are 3-dimensional algebraic structures that control quantum link polynomials and that give rise to 3-manifold invariants known as skein modules. I will describe how to use Khovanov-Rozansky link homology, a categorification of the gl(N) quantum link polynomial, to obtain a 4-dimensional algebraic structure that gives rise to vector space-valued invariants of smooth 4-manifolds. The technical heart of this construction is the newly established functoriality of Khovanov-Rozansky homology in the 3-sphere. Based on joint work with Scott Morrison and Kevin Walker