We extend Bar-Natan's cobordism-based categorification of the Jones polynomial to virtual
links. Our topological complex allows a direct extension of the classical Khovanov complex …

This thesis splits into two major parts. The connection between the two parts is the notion of"
categorification" which we shortly explain/recall in the introduction. In the first part of this …

We define a homology theory of virtual links built out of the direct sum of the standard
Khovanov complex with itself, motivating the name doubled Khovanov homology. We …

We give a fresh introduction to the Khovanov Homology theory for knots and links, with
special emphasis on its extension to tangles, cobordisms and 2–knots. By staying within a …

Khovanov homology is a powerful link invariant: a categorification of the Jones polynomial
that enjoys a rich and beautiful algebraic structure. This homology theory has been …

The Jones polynomial and Khovanov homology of a classical link are invariants that depend
upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology …

The paper contains an essentially self-contained treatment of Khovanov homology,
Khovanov–Lee homology as well as the Rasmussen invariant for virtual knots and virtual …

We construct an algebra of nontrivial homological operations on Khovanov homology with
coefficients in ℤ 2 generated by two Bockstein operations. We use the unified Khovanov …

We reconsider the link homology theory defined by Knovanov in [9] and generalized by
Mackaay and Vaz in [15]. With some slight modifications, we describe the theory as a map …

Quasi-alternating links are a natural generalization of alternating links. In this paper, we
show that quasi-alternating links are" homologically thin" for both Khovanov homology and …