GAUGE-THEORIES - GEOMETRY AND COHOMOLOGICAL INVARIANTS

We develop a geometrical structure of the manifolds Gamma and <(Gamma) over cap> associated, respectively, with gauge symmetry and BRST symme try. Then, we show that (<(Gamma)over cap>, <(zeta)over cap>, Gamma), where <(zeta)over cap> is the group of BRST transformations, is endowe d with the structure of a principal fiber bundle over the base manifol d Gamma. Furthermore, in this geometrical setup, due to the nilpotency of the BRST operator, we prove that the effective action of a gauge t heory is a BRST-exact term up to the classical action. Then, we conclu de that the effective action where only the gauge symmetry is fixed is cohomologically equivalent to the action where the gauge and the BRST symmetries are fixed.