  We investigate how the multiple bands of fermions on a crystal lattice evolve
if a magnetic field is added which does not increase the number of bands. The
kagome lattice is studied as generic example for a lattice with loops of three
bonds. Finite Chern numbers occur as non-trivial topological property in
presence of the magnetic field. The symmetries and periodicities as function of
the applied field are discussed. Strikingly, the dispersions of the edge states
depend crucially on the precise shape of the boundary. This suggests that
suitable design of the boundaries helps to tune physical properties which may
even differ between upper and lower edge. Moreover, we suggest a promising
gauge to realize this model in optical lattices.
