U(1)^n Chern-Simons partition functions coincide, up to normalization, with Reshetikhin-Turaev invariants built from a twisted (non-modular) category.
A reciprocity formula from abelian BF and Turaev-Viro theories
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abstract
In this article we show that the use of Deligne-Beilinson cohomology in the context of the $U(1)$ BF theory on a closed 3-manifold $M$ yields a discrete $\Z_N$ BF theory whose partition function is an abelian TV invariant of $M$. By comparing the expectation values of the $U(1)$ and $\mathbb{Z}_N$ holonomies in both BF theories we obtain a reciprocity formula.
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Reshetikhin-Turaev construction and $\mathrm{U}(1)^n$ Chern-Simons partition function
U(1)^n Chern-Simons partition functions coincide, up to normalization, with Reshetikhin-Turaev invariants built from a twisted (non-modular) category.