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We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl( N ) knot polynomial due to Murakami, Ohtsuki, and Yamada. We discuss how the resulting moduli space can be thought of a representation variety. We show that the Euler characteristic of the moduli space is equal to the quantum sl( N ) polynomial of the graph evaluated at unity. Possible extensions of the result are also indicated.

The Quantum sl( N ) Graph Invariant and a Moduli Space