We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also present a spanning quasi-tree model for the Khovanov homology of a ribbon graph.
Publication Source (Journal or Book title)
Dasbach, O., & Lowrance, A. (2014). A Turaev surface approach to Khovanov homology. Quantum Topology, 5 (4), 425-486. https://doi.org/10.4171/QT/55