Plumbing essential states in Khovanov homology (Q1670709)

This paper explores an important and interesting topic, that is, what does a non-zero Khovanov homology class look like? It starts with the simplest examples, adequate links, and mentions the essential property of an adequate state in the sense that the state surfaces of non-zero homology classes are incompressible and \(\partial\)-incompressible. Then the main question of the paper is to find for which essential state \(x\) the subchain complex \(C_{R}(x)\) contains a non-zero homology class. The author's main result is that Khovanov homology over \(\mathbb{Z}_{2}\) detects all homogeneously adequate states. The author gives a direct proof and another approach with a more geometric motivation that allows the author to define plumbing in Khovanov homology on the level of chain complexes of chosen states.