We investigate Khovanov homology of stable equivalence classes of link diagrams on
oriented surfaces. We apply Bar-Natan's geometric formalism to this setting and using …

Using derived categories of equivariant coherent sheaves, we construct a categorification of
the tangle calculus associated to sl (2) and its standard representation. Our construction is …

Khovanov homology generalizes the Jones polynomial as knot invariant. The challenge is to
find a quantum physical construction of Khovanov homology analous to the topological QFT …

We propose a framework for unifying the sl (N) Khovanov–Rozansky homology (for all N)
with the knot Floer homology. We argue that this unification should be accomplished by a …

In this paper, we prove that every Khovanov homology associated to a Frobenius algebra of
rank 2 can be modified in such a way as to produce a TQFT on oriented links, that is a …

Using techniques from [14] we construct topological quantum field theories using an
algebraic model of a homotopy 2-type as initial data. In [14] the author, motivated by work of …

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 …

In this paper we present an explicit isomorphism between Khovanov–Rozansky sl2-
homology and ordinary Khovanov homology. This result was originally claimed in Khovanov …

Using methods suggested by the work of Turaev and Viro [11, 12], we provide a detailed
construction of topological quantum field theories associated to finite crossed G-sets. Our …

This paper is devoted to the study of algebraic structures leading to link homology theories.
The originally used structures of Frobenius algebra and/or TQFT are modified in two …