Pedro Dos Santos Santana Forte Vaz

The universal sl3–link homology

We define the universal sl3 –link homology, which depends on 3 parameters, following Khovanov’s approach with foams. We show that this 3–parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov’s original sl3 –link homology belongs, the second is the one studied by Gornik in the context of matrix factorizations and the last one is new. Following an approach similar to Gornik’s we show that this new link homology can be described in terms of Khovanov’s original sl2 –link homology.

sl.N/-link homology (N 4) using foams and the Kapustin-Li formula

We use foams to give a topological construction of a rational link homology categorifying the slN link invariant, for N>3. To evaluate closed foams we use the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that for any link our homology is isomorphic to Khovanov and Rozanskys.

A remark on rasmussen's invariant of knots

We show that Rasmussens invariant of knots, which is derived from Lees variant of Khovanov homology, is equal to an analogous invariant derived from certain other filtered link homologies.

The 1,2-coloured HOMFLY-PT link homology

In this paper we define the 1,2-coloured HOMFLY-PT triply graded link homology and prove that it is a link invariant. We also conjecture on how to generalize our construction for arbitrary colours.

Super q-Howe duality and web categories

We use super

A diagrammatic categorification of the q-Schur algebra

q

The foam and the matrix factorization sl3 link homologies are equivalent

-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of

The Diagrammatic Soergel Category and sl(2) and sl(3) Foams

\mathfrak{gl}_N

The Diagrammatic Soergel Category and sl(N)-Foams, for N≥4

-modules (and, more generally,

On 2-Verma modules for quantum \({\mathfrak {sl}_{2}}\)

\mathfrak{gl}_{N|M}