Topological Study of Global Quantization in Non-Abelian Gauge Theories

We study some topological aspects of non-abelian gauge theories intimately connected to the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection to the non-perturbative solution to strong CP problem as originally proposed by the author is also discussed. Some relevant topological formulas are also given and discussed. A result from the physics application is that the usual gauge orbit space on the compactified space can contain at most a $Z_2$ monopole structure in the SP(2N) gauge theories. Some relevance to the open universe is also discussed. We expect that our results may also be useful to the other studies of non-abelian gauge theories in general.