A Turaev surface approach to Khovanov homology
Oliver T. Dasbach, Adam M. Lowrance
TL;DR
This paper introduces a new approach to Khovanov homology using Turaev surfaces and ribbon graphs, establishing an isomorphism with link Khovanov homology and providing a spanning quasi-tree model.
Contribution
It presents a novel Turaev surface method for computing Khovanov homology of ribbon graphs, linking it to link invariants and offering a new combinatorial model.
Findings
Khovanov homology of a ribbon graph on a Turaev surface is isomorphic to that of the link
A spanning quasi-tree model for ribbon graph Khovanov homology is developed
The approach unifies link and graph invariants through topological surfaces
Abstract
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.
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