  We address the question of whether fractionally filled bands with a
nontrivial Chern index in zero external field could also exhibit a Fractional
Quantum Hall Effect (FQHE). Numerical works suggest this is possible. Analytic
treatments are complicated by a non-vanishing band dispersion and a
non-constant Berry flux. We propose embedding the Chern band in an auxiliary
lowest Landau level (LLL) and then using composite fermions. We find some
states which have no analogue in the continuum, and dependent on the interplay
between interactions and the lattice. The approach extends to two-dimensional
time-reversal invariant topological insulators.
