ScalingStacks

Theorem 1.1. Suppose that we have a four-manifold $W$ with boundary $Y$, and let $W^{\prime}$ be the result of attaching a 3-handle to $W$ along a sphere $S\subset Y$. Let also $L$ be a framed link in $Y$ disjoint from $S$, and $L^{\prime}$ the corresponding link in $\partial W^{\prime}$. The equator $J$ of $S$ splits the sphere into two hemispheres, each of which induces a cobordism map from $\mathcal{S}_{0}^{N}(W;L\cup J)$ to $\mathcal{S}_{0}^{N}(W;L)$. Then, the skein lasagna module $\mathcal{S}_{0}^{N}(W^{\prime};L^{\prime})$ is isomorphic to the coequalizer of these two cobordism maps. (See Theorem 3.7 for a more precise statement.)