Fractional quantum numbers, complex orbifolds and noncommutative geometry

Abstract

This paper studies the conductance on the universal homology covering space Z of 2D orbifolds in a strong magnetic field, thereby removing the rationality constraint on the magnetic field in earlier works [3, 29, 25] in the literature. We consider a natural Landau Hamiltonian on Z and study its spectrum which we prove consists of a finite number of low- lying isolated points and calculate the von Neumann degree of the associated holomorphic spectral orbibundles when the magnetic field B is large, and obtain fractional quantum numbers as the conductance.