Symmetries of equivariant Khovanov-Rozansky homology

Abstract

We construct an ${\mathfrak{sl}}_2$-action on equivariant ${\mathfrak{gl}}_N$-link homologies. As a consequence we obtain an action of ${\mathfrak{sl}}_2$ on these homologies as well as a $p$-DG structures for $p$ a prime number. We explore topological applications of these structures.

53 pages, many figures. Comments welcome! 2nd version removes a mistakes in the topological applications of the construction. v3: small changes of conventions for crossings, 54 pages