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