The branch process of skyrmions in the fractional quantum Hall effect

The branch process of the skyrmions in the fractional quantum Hall effect is studied from the phi-mapping topological current. It is shown that there exists a field zeta whose Hopf indices and Brouwer degrees characterize the topological structure of the skyrmions. Based on the bifurcation theory of the phi-mapping theory, it is found that the skyrmions can be generated or annihilated at the limit points and they encounter, split or merge at the bifurcation points of the new field zeta.