Cohomology of gauge fields and explicit construction of Wess-Zumino lagrangians in nonlinear sigma models over G/H

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By generalizing the well-known Chern-Weil and Chern-Simons theorems, we are able to define a tower of cocycles in the entire space of gauge potentials. This construction not only induces (though not directly) the usual tower of cocycles on a gauge orbit, but also generates nontrivial cocycles, by appropriate projection, in the gauge-orbit space. As an application, using the Chern-Simons one-cocycle in this new tower, we explicitly construct the Wess-Zumino action in nonlinear sigma models over a homogeneous space G/H in any even dimensions.