  Geometric realization of opinion is considered as a simplex and the opinion
space of a group of individuals is a simplicial complex whose topological
features are monitored in the process of opinion formation. The agents are
physically located on the nodes of the scale-free network. Social interactions
include all concepts of social dynamics present in the mainstream models
augmented by four additional interaction mechanisms which depend on the local
properties of opinions and their overlapping properties. The results pertaining
to the formation of consensus are of particular interest. An analogy with
quantum mechanical pure states is established through the application of the
high dimensional combinatorial Laplacian.
