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 define an invariant of oriented links in S 3 using the symplectic geometry of certain
spaces that arise naturally in Lie theory. More specifically, we present a knot as the closure …

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

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 …

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 …

We propose a way of computing 4-manifold invariants, old and new, as chiral correlation
functions in half-twisted 2d N=(0, 2) theories that arise from compactification of fivebranes …

The purpose of this paper is to study categorifications of tensor products of finite-
dimensional modules for the quantum group for sl _2. The main categorification is obtained …

We show that Khovanov homology (and its sl 3 variant) can be understood in the context of
higher representation theory. Specifically, we show that the combinatorially defined foam …

14 a prehistory of n-categorical physics just categories and bicategories). We also include a
review of some relevant aspects of twentieth-century physics. The most obvious roads to n …

In a previous work, we constructed a spectrum-level refinement of Khovanov homology. This
refinement induces stable cohomology operations on Khovanov homology. In this paper we …