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We study some topological aspects of non-abelian gauge theories intimatelyconnected to the Lie algebras of the gauge groups and the homotopy theory inthe generalized gauge orbit space. The physics connection to thenon-perturbative solution to strong CP problem as originally proposed by theauthor is also discussed. Some relevant topological formulas are also given anddiscussed. A result from the physics application is that the usual gauge orbitspace on the compactified space can contain at most a $Z_2$ monopole structurein the SP(2N) gauge theories. Some relevance to the open universe is alsodiscussed. We expect that our results may also be useful to the other studiesof non-abelian gauge theories in general.Comment: JSUHEP930701, LaTeX 17 page

TOPOLOGICAL STUDY OF GLOBAL QUANTIZATION IN NON-ABELIAN GAUGE THEORIES AND THE OPEN UNIVERSE