Graphs, foams, homology, polytopes and abstract tensors

The operations of conjugation and multiplication in a group satisfy four properties that can be interpreted as moves on knotted trivalent graphs that represent handle-body knots. These moves are codimension 1 singularities. The codimension 2 singularities give rise to movie moves for knotted foams. These movie moves are chains in a higher dimensional homology theory. The pictures then can be dualized to produce polytopes and analyzed from the point of view of abstract tensors. A system of equations arises that has a nice solution from the above considerations.