Abstract
We use a model of constant negative curvature Riemann surfaces to study the effect of coupling together several Hall systems on the Hall conductances of the individual systems. We find that on average, the coupling does not effect the conductances. The method we use is based on the fact that the average conductances are given by Chern numbers, and hence are stable when one varies parameters of the Hamiltonian, as long as eigenvalues do not cross. The parameters we change are the surface parameters, and we find the averaged conductances of the surface by 'twisting' and 'pinching' it. This method is applicable to other systems as well.
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