ScalingStacks

Then, the skein lasagna module $\mathcal{S}_{0}^{N}(W_{4};L,\alpha^{\prime})$ is isomorphic to the quotient of the direct sum of cabled skein lasagna modules $\bigoplus_{\alpha\in\langle\alpha^{\prime}\rangle}\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N,\alpha}(W_{1};K,L)$ by the relations

(14)

$$\underline{\Psi}_{I\times\partial W_{1};\Sigma_{j}(n\bullet),\alpha^{\prime}}(v)=0,\ \ n=0,1,\dots,N-2,$$

and

(15)

$$\underline{\Psi}_{I\times\partial W_{1};\Sigma_{j}((N-1)\bullet),\alpha^{\prime}}(v)=v$$

for all $v\in\bigoplus_{\alpha\in\langle\alpha^{\prime}\rangle}\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N,\alpha}(W_{1};K,L)$ and $j=1,\dots,p$.