Main accomplishers: Guang-Zhao Zhou，Han-Ying Guo，Bo-Yu Hou，Hang-Zhang Song，Ke Wu，Bo-Yuan Hou，Shi-Kun Wang

The project on global properties of gauge theory and its effective theory, won the honor of National Natural Science Award (second class), P.R.China in 1989. A series of systematic studies in-depth have been carried in the following aspects: The gauge field theory and its effective theory, especially on the global properties of the gauge anomalies, such as the correct expression and existence condition for the “anomalous” term in the Wess-Zumino-Witten gauge invariant effective theory; The relations among the non-Abelian anomaly of 2n dimensions, the Chern-Simons secondary characteristic class of 2n+1 dimensions and the Abelian anomaly of 2n+2 dimensions; The generalized Chern – Simons classes and related double complex, that is, the general co-chains for the zig-zag equation ; based upon these co-chains the gauge group co-homological analysis and so on.