  This paper studies the conductance on the universal homology covering space
$Z$ of 2D orbifolds in a strong magnetic field, thereby removing the
integrality constraint on the magnetic field in earlier works in the
literature. We consider a natural Landau Hamiltonian on $Z$ and show that its
low-lying spectrum consists of a finite number of isolated points. We 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.
