Gauge Group and Topology Change

The purpose of this study is to examine the effect of topology change in the initial universe. In this study, the concept of $G$-cobordism is introduced to argue about the topology change of the manifold on which a transformation group acts. This $G$-manifold has a fiber bundle structure if the group action is free and is related to the spacetime in Kaluza-Klein theory or Einstein-Yang-Mills system. Our results revealed that fundamental processes of compactification in $G$-manifolds. In these processes, the initial high symmetry and multidimensional universe changes to present universe by the mechanism which lowers the dimensions and symmetries.