Algebra and Topology Seminar, Title of the talk: *Functoriality of the Khovanov homology*, Australian National University, Australia, October 9, 2018

Abstract: In 1999 Khovanov assigned to a knot (or link) a complex whose homotopy type is a link invariant and whose Euler characteristic is the Jones polynomial. This construction is known as a categorification of the Jones polynomial. Actually links form a category, whose morphisms are surfaces bounding links. The Khovanov homology extends to a functor from this category to the category of chain complexes, which is well-defined only up to sign. In the talk, after briefly recalling Khovanov’s construction, I will explain how to make it truly functorial. More precisely, I will construct an equivalence between the Bar-Natan tangle category and the category of gl(2)-foams. This is a joint work with K. Putyra, M. Hogancamp and S. Wehrli.