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In this note we make an attempt to compare a cohomological theory of Hilbertspaces of ground states in the ${\cal N}=(2,2)$ 2d Landau-Ginzburg theory inmodels describing link embeddings in ${\mathbb{R}}^3$ to Khovanov andKhovanov-Rozansky homologies. To confirm the equivalence we exploit theinvariance of Hilbert spaces of ground states for interfaces with respect tohomotopy. In this attempt to study solitons and instantons in theLandau-Giznburg theory we apply asymptotic analysis also known in theliterature as exact WKB method, spectral networks method, or resurgence. Inparticular, we associate instantons in LG model to specific WKB lineconfigurations we call null-webs.

Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?