Invariants of 4–manifolds from Khovanov–Rozansky link homology

Abstract

We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of 𝔤𝔩 𝑁 link homology, for which we prove non-vanishing and decomposition results.