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On three-dimensional topological field theories constructed from $D^ω(G)$ for finite group

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation $\D{G}$ of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by $\zcfs = |\zdw|^2$ when $G=\Z_{2N+1}$. For $G=\Z_{2N}$, such a relation does not hold.