Georgia Institute of Technology College of Sciences

Skein lasagna modules are smooth 4-manifold invariants constructed from functorial link homology theories. These invariants are capable of detecting exotic phenomena in dimension 4. Wall-type stabilization questions ask about the behavior of exotic smooth structures under various topological operations. In studying applications of these invariants to Wall-type stabilization problems, we construct an isomorphism between the skein lasagna invariant of a pair of the form (S^2xD^2, L), where L is a link in the boundary S^1xS^2, and the Rozansky-Willis homology of L in S^1xS^2 up to an extra tensor factor. In this talk, we will describe both invariants, describe their relationship, and discuss relevant properties. We will then briefly sketch how the properties of skein lasagna modules are used to establish functoriality for Rozansky-Willis homology and how to upgrade the theory to a new 4-manifold invariant.