STATE SUM MODELS FOR TRIVALENT KNOTTED GRAPH INVARIANTS USING QUANTUM GROUP SLq(2)

Four approaches to construct polynomial invariants for trivalent knotted graphs in S3 are compared. The first approach is based on vertex model with R-matrices and Glebsh-Gordan coefficients, appearing in SLq(2)-representations theory, as Boltzman weights. The second approach is based on Kauffman's quantum spin network theory, the third one is based on Witten-Turaev area-coloring model (or face model) based on quantum 6j-symbols, where q is root of unity. The fourth approach is based on the same face (or area-coloring) model, but q is not root of unity. The coincidence (up to certain normalization) of topological invariants, arising from these four state models, is proved.