ScalingStacks

Remark 5.5. If $L$ represents a non-zero class in $H_{1}(W)$, then we have $\mathcal{S}^{N}_{0}(W;L)=\emptyset$ since there are no compatible lasagna fillings. It would be interesting to relate $\mathcal{S}^{N}_{0}$ to $\mathfrak{gl}_{N}$ versions of the invariants of links in $S^{2}\times S^{1}$ or $(S^{2}\times S^{1})^{\#g}$ constructed by Rozansky [Roz10] and Willis [Wil21] respectively, which are trivial for homologically non-zero links.