Quasi-invariants of 2-knots and integrable 3-d statistical models

I'l talk about recent works with Korepanov and Sharygin investigating so-called $n$-simplicial complexes, their cohomologies and special statistical models on graphs with 6-valent vertexes. These models are integrable if one considers regular periodic lattices and provide quasi invariants of 2-knots being restricted to the graph of singular points of a 2-knot diagram.