An action of the Witt algebra on Khovanov-Rozansky homology

Abstract

We construct an action of the positive part of the Witt algebra on Khovanov--Rozansky $\mathfrak{gl}_N$-link homology and show that link cobordisms induce equivariant maps between twists of the homology. Moreover, the state spaces of simple webs are identified with standard representations of the Witt algebra on polynomials. Some simple relations to Lee homology and genus bounds are derived from the analysis of this presentation.