External edge condition and group cohomologies associated with the quantum Clebsch-Gordan condition
arXiv:0708.4190
Abstract
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 by the author in the study of the Heisenberg representation on the TQFT-module.
arXiv comment9 pages, 6 figures ; introduction revised ; comment before theorem 4.3 added ; remark 4.3 deleted ; statements in section 5 improved ; reference updated ; to appear in Kyushu Journal of Mathematics