Topological structure and evolution of space-time dislocations and disclinations

By making use of the gauge potential decomposition theory and phi-mapping theory, the topological structure and the topological quantization of dislocations and disclinations are studied in the framework of Riemann-Cartan space-time manifold. The evolution of dislocation strings and disclination points is also studied from the topological properties of the order parameter field. The dislocations and disclinations are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the order parameter field.