Comparing a new homology theory for trivalent graphs with Khovanov homology for virtual links

In this lecture, I will show how to categorify the 2-factor polynomial to get a homology theory of trivalent ribbon graphs with perfect matchings. The 2-factor polynomial is useful in graph theory because it counts certain 3-edge colorings of a graph. I will then introduce the notion of a graphene, which is an equivalence class of ribbon graphs that behaves like a virtual link. Finally, I will compare the homology theory to Khovanov homology of virtual links using graphenes and show that, while the two share many similarities, they are different theories.
The work on graphenes is joint with Lou Kauffman and Will Rushworth.