MODULAR-GROUPS, VISIBILITY DIAGRAM AND QUANTUM HALL-EFFECT

We consider the action of the modular group Gamma(2) on the set of pos itive rational fractions. From this, we derive a model for a classific ation of Fractional (as well as integer) Hall states which can be visu alized on two 'visibility' diagrams, the first one being associated wi th even denominator fractions whereas the second one is linked to odd denominator fractions. We use this model to predict, among some intere sting physical quantities, the relative ratios of the width of the dif ferent transversal resistivity plateaus. A numerical simulation of the tranversal resistivity plot based on this last prediction fits well w ith the present experimental data.