A spectral sequence for Khovanov homology with an application to (3,q)-torus links (Q929204)

The Khovanov homology [\textit{M. Khovanov}, Duke Math. J. 101, No.~3, 359--426 (2000; Zbl 0960.57005)] \(\text{KH}^{i,j}(L)\) of a link \(L\) is a categorification of the Jones polynomial \(V(L;q)\), that is, the graded Euler characteristic \(\sum_{i,j}(-1)^i q^j \dim \text{KH}^{i,j}(L)\) equals \(V(L;q)\). Since the Jones polynomial can be defined by using the Kauffman bracket, it satisfies the Kauffman skein relation, a linear relation among a link diagram and two diagrams obtained by resolving a crossing in two ways. The corresponding exact sequence for the Khovanov homology is noted in [\textit{O. Viro}, Fundam. Math. 184, 317--342 (2004; Zbl 1078.57013)]. In the paper under review, the author extends this exact sequence to a spectral sequence converging to the Khovanov homology. As an application the (rational) Khovanov homology of the torus link of type \((3,q)\) is calculated.