  We introduce Deligne cohomology that classifies U(1) fibre bundles over
3-manifolds endowed with connections. We show how the structure of Deligne
cohomology classes provides a way to perform exact (non-perturbative)
computations in U(1) Chern-Simons theory (resp. BF theory) at the level of
functional integrals. The partition functions (and observables) of these
theories are strongly related to topological invariants well-known by the
mathematicians.
