  In the light of $\phi$-mapping method and topological current theory, the
topological structure and the topological quantization of topological linear
defects are obtained under the condition that the Jacobian $J(\phi/v) \neq 0$.
When $J(\phi/v) = 0$, it is shown that there exist the crucial case of branch
process. Based on the implicit function theorem and the Taylor expansion, the
origin and bifurcation of the linear defects are detailed in the neighborhoods
of the limit points and bifurcation points of $\phi$-mapping, respectively.
