We use a special kind of 2-dimensional extended Topological Quantum Field Theories
(TQFTs), so-called open-closed TQFTs, in order to represent a refinement of Bar-Natan's …

We describe a" concentration on the diagonal" condition on the Khovanov complex of
tangles, show that this condition is satisfied by the Khovanov complex of the single crossing …

We determine the algebraic structure underlying the geometric complex associated to a link
in Bar-Natan's geometric formalism of Khovanov's link homology theory (n= 2). We find an …

We further study the symplectic Khovanov homology of Seidel and Smith and its
generalization to even tangles. This homology theory is a conjectural geometric model for …

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 …

We give an alternative presentation of Khovanov homology of links. The original
construction rests on the Kauffman bracket model for the Jones polynomial, and the …

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 …

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 …

• In particular, there is an associated invariant of 2-knots and 2-links in 4-space.• Much is
known about generalizations and relations of the Jones polynomial, but little is known about …

It has already been rigorously established that if G is a finite group and α∈ H4 (G; ℤ), there
is an associated 2+ 1-dimensional topological quantum field theory. In the case α= 0, there …