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In the generalized topological quantum field theory constructed by Andersen and Kashaev, invariants of 3-manifolds are defined given the combinatorial structure of a tetrahedral decomposition. Furthermore, a variant of the volume conjecture has been proposed in which the hyperbolic volume can be extracted from this invariant of the complementary space of the hyperbolic knot in an oriented -dimensional closed manifold. We prove that the reformulated volume conjecture holds for the complementary space of the hyperbolic knot in , given a specific tetrahedral decomposition.

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