On the quantum Hall effect for Dirac fermions

The QHE for Schrödinger particles (electrons described by a Schrödinger operator) in strong magnetic fields results in the quantisation of conductance. The remarkable stability of this effect can be traced back to its topological nature. We describe a QHE for Dirac fermions which is present even without a magnetic field. In a simple concrete example we analyze the connections with geometry and topology. Part of the results are joint work with Marianne Leitner and Ruedi Seiler.