Khovanov homology and oriented ribbon graphs

Adam Lowrance (Vassar)

Abstract: We define Khovanov homology of ribbon graphs and discuss how it ties together the Khovanov homology of both classical and virtual links. The spanning tree complex of Khovanov homology generalizes in the ribbon graph setting to a quasi-tree complex, which shows a relation between the Khovanov homology (of both classical and virtual links) and Turaev genus. We also discuss ribbon graph Reidemeister moves and discuss how they may be used to give distinct virtual links with isomorphic Khovanov homology.