Abstract
Based upon the properties of the characteristic classes and their Chern-Simons secondary characteristic classes, the Abelian anomalies in , the Euler-Heisenberg effective actions in , as well as the non-Abelian anomalies in for arbitrary gauge group and its reduction subgroup have been investigated thoroughly and the application to the gravitational anomalies is made. It is shown that the Abelian anomalies of such groups are equal to each other, their Eu1er-Heisenberg actions are also closely related to each, other, and their non-Abelian anomalies are also equivalent if their common generating functional can be taken as a counter-term. For the gravitational anomalies we present the common generating functional for both non-Abelian Einstein and Lorentz anomalies in and show the relationship between them.
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