Topological Features of the Magnetic Response in Inhomogeneous Magnetic Fields

We present topological features of the magnetic response (orbital and spin) of a two-dimensional degenerate and non interacting electron gas due to inhomogeneous applied magnetic fields. These issues are analysed from the point of view of the Index theory with a special emphasis on the non perturbative aspects of this response. The limiting case of a Aharonov-Bohm magnetic flux line is studied in details and the results are extended to more general situations.