Hall conductance and adiabatic charge transport of leaky tori

Leaky tori are two-dimensional surfaces with g handles and r horns (punctures) that extend to infinity. They model certain features of mesoscopic systems with multiple Aharonov-Bohm-type geometries connected to infinitely long leads. For a large class of leaky tori with finite area, in the presence of a constant magnetic field and threading fluxes, we calculate exactly the persistent currents, adiabatic charge transport, and the (appropriately defined) Hall conductances.