Deligne-Beilinson Cohomology and Abelian Link Invariants

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 link invariants in the case of the torsion-free 3-manifolds S-3, S-1 x S-2 and S-1 x Sigma(g).