  We investigate the interaction of magnetic vortices and skyrmions with a
spin-polarized current. In a square lattice, fixed classical spins and quantum
itinerant electrons, evolve according to the coupled Landau-Lifshitz and
Schr\"odinger equations. Changes in the topology occur at microscopic time and
length scales, and are shown to be triggered by the nucleation of a nontrivial
electron-spin structure at the vortex core.
