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$G$ cocycle split and trivialized to a coboundary in $J$, given a group homomorphism $J \overset{r}{\rightarrow} G$
Consider a generic nontrivial 3-cocycle $\omega_3^G(g_1,g_2,g_3) \in H^3(G,U(1))$ in the cohomology group of $G$ with $U(1)=\mathbb{R}/\mathbb{Z}$ coefficient. In otherwords, here the 3-cocycle $\...
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