The topological structure of the vortices in the O(n) symmetric TDGL model

In the light of $\phi $--mapping method and topological current theory, the topological structure of the vortex state in TDGL model and the topological quantization of the vortex topological charges are investigated. It is pointed out that the topological charges of the vortices in TDGL model are described by the Winding numbers of $\phi $--mapping which are determined in terms of the Hopf indices and the Brouwer degrees of $\phi $--mapping.