Genus bounds from skein lasagna

Khovanov homology extends to an invariant of smooth oriented 4-manifolds, which is defined as a skein module spanned by decorated embedded surfaces, modulo local relations. I will introduce equivariant and Lee versions of these skein modules and compute the latter. This leads to a non-vanishing result for certain skein classes in the former and, as a consequence, to analogs of Rasmussen's s-invariant for smooth surfaces in a given (relative) second homology class of a 4-manifold. Based on joint work with Scott Morrison and Kevin Walker.