Fractional Quantum Hall Effect, Jain's Rule, and Topological Textures

It is demonstrated that Jain's rule for determining fractions in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility of existence is considered for topologically nontrivial many-electron wave functions, whose group classification gives an indication of special values of electron density in the ground states separated by a gap from excited energies.