Virtual knot theory is an extension of classical knot theory to stabilized embeddings of circles
into thickened orientable surfaces of genus possibly greater than zero. Classical knot theory …

Khovanov homology and the slice genus Page 1 Invent math (2010) 182: 419–447 DOI
10.1007/s00222-010-0275-6 Khovanov homology and the slice genus Jacob Rasmussen …

To a presentation of an oriented link as the closure of a braid we assign a complex of
bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded …

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 …

Over the last fifteen years, the face of knot theory has changed due to various new theories
and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to …

We consider a class of bimodules over polynomial algebras which were originally
introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct …

We introduce a local algorithm for Khovanov homology computations—that is, we explain
how it is possible to" cancel" terms in the Khovanov complex associated with a (" local") …

The first two sections of the paper provide a convenient scheme and additional
diagrammatics for working with Frobenius extensions responsible for key flavors of …

It is known that knot homologies admit a physical description as spaces of open BPS states.
We study operators and algebras acting on these spaces. This leads to a very rich story …

We give an elementary construction of colored sl n link homology. The invariant takes values
in a 2-category where 2-morphisms are given by foams, singular cobordisms between sl n …