Vortex lattices as a key model for the fractional quantum Hall effect.

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The necessary additional flux is supplied by the vortex lattice, which allows us to consider all fractions in a unified frame. The group classification predicts the electron density of the ground state and the existence of a gap that separates it from excited states. This gap was calculated for some lattices in a simplified model.