Caltech/USC/UCLA Joint Topology Seminar

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.