  Hall conductance of noninteracting fermions filling a certain number of
Landau levels can be written as a topological invariant. A particular version
of this invariant when expressed in terms of the single particle Green's
functions directly generalizes to cases when interactions are present including
those of fractional Hall states, although in those cases this invariant no
longer corresponds to Hall conductance. We argue that when evaluated in
fractional Hall states this invariant gives twice the total orbital spin of
fermions which in turn is closely related to the Hall viscosity, a quantity
characterizing the integer and fractional Hall states which recently received
substantial attention in the literature.
