U(1)^n Chern-Simons partition functions coincide, up to normalization, with Reshetikhin-Turaev invariants built from a twisted (non-modular) category.
Deligne-Beilinson cohomology and abelian links invariants
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abstract
For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit path-integral non-perturbative computation of the Chern-Simons links invariants in the case of the torsion-free 3-manifolds $S^3$, $S^1 \times S^2$ and $S^1 \times \Sigma_g$.
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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.