Theorem 1.2 (0NFJ) · ScalingStacks

Theorem 1.2. Consider four-manifolds $W_{1}\subseteq W_{2}\subseteq W_{3}\subseteq W_{4}$ where

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$W_{1}=\natural^{m}(S^{1}\times B^{3})$ is the union of $m$ one-handles;
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$W_{2}$ is obtained from $W_{1}$ by attaching $n$ two-handles along a framed link $K$ ;
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$W_{3}$ is obtained from $W_{2}$ by attaching $p$ three-handles along spheres $S_{1},\dots S_{p}$ ;
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$W_{4}$ be obtained from $W_{3}$ by attaching some four-handles.

Consider also a framed link $L\subset\partial W_{4}$ , and view $K\cup L$ as a link in $\partial W_{1}$ . Then, the skein lasagna module $\mathcal{S}_{0}^{N}(W_{4};L)$ is isomorphic to the quotient of the cabled skein lasagna module $\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N}(W_{1};K,L)$ by coequalizing relations coming from the 3-handles as in Theorem 1.1. (See Theorem 3.10 for a more precise statement.)