ABSTRACT

This chapter discusses one of the first striking applications of the Khovanov homology, the Rasmussen invariant. It explains the Lee homology, which has the same pattern as the Khovanov homology, and leads to just two non-trivial generators for the case of a knot. Then the story starts, and the Khovanov homology can be considered as the starting term of the spectral sequence which converges to the Lee homology. There is one important class of virtual links where the whole contents of the chapter generalises straightforwardly even virtual links or virtual links with orientable atoms. In fact, the only thing one needs to construct the Lee-Rasmussen is the source-sink structure of the atom.