Cocycles in topological Yang-Mills theories

The authors show that the cocycles arise in the Yang-Mills theories with topological terms added. They are found in the representation of the translation group in the configuration space or gauge orbit space, and are shown to be directly related to the U(1) functional connection in these spaces. In 3 + 1 dimensions, if they adopt a vector representation (i.e. vanishing 2-cocycle), the authors find the θ-parameter in the Pontryagin term to be 2π x integers. While, in 2 + 1 dimensions, insisting that finite translations be associative (i.e., vanishing 3-cocycle) leads to the known quantization of the topological mass. Some related aspects with anomalies are also discussed