Invariants of surfaces in smooth 4-manifolds from link homology

Scott Morrison, Kevin Walker, Paul Wedrich

Published 2024-01-12Version 1

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 $\mathfrak{gl}_N$ link homology, for which we prove non-vanishing and decomposition results.