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Deligne-Beilinson cohomology and abelian links invariants

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arxiv 0801.1445 v2 pith:7K64FQLG submitted 2008-01-09 math-ph math.MP

Enore Guadagnini (df) , Frank Thuillier (LAPTH) This is my paper · ORCID
classification math-phmath.MP
keywords abelianchern-simonscohomologydeligne-beilinsoninvariantslinkstimescase
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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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  1. Reshetikhin-Turaev construction and $\mathrm{U}(1)^n$ Chern-Simons partition function

    math-ph 2025-07 conditional novelty 6.0 of 10

    U(1)^n Chern-Simons partition functions coincide, up to normalization, with Reshetikhin-Turaev invariants built from a twisted (non-modular) category.

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