  We consider charge transport for interacting many-body systems with a gapped
ground state subspace which is finitely degenerate and topologically ordered.
To any locality-preserving, charge-conserving unitary that preserves the ground
state space, we associate an index that is an integer multiple of $1/p$, where
$p$ is the ground state degeneracy. We prove that the index is additive under
composition of unitaries. This formalism gives rise to several applications:
fractional quantum Hall conductance, a fractional Lieb-Schultz-Mattis theorem
that generalizes the standard LSM to systems where the translation-invariance
is broken, and the interacting generalization of the Avron-Dana-Zak relation
between Hall conductance and the filling factor.
