External edge condition and group cohomologies associated with the quantum clebsch-gordan condition

摘要

In this article we determine the structure of a twisted first cohomology group of the first homology of a trivalent graph with a coefficient associated with the quantum Clebsch- Gordan condition. As an application we give a characterization of a combinatorial property, the external edge condition, which is defined in the study of the Heisenberg representation on the module constructed in the framework of topological quantum field theory, i.e. TQFTmodule.