  We consider two-dimensional electron systems in zero magnetic field at
fractional filling. For such systems a Lieb-Schultz-Mattis theorem applies,
forbidding the existence of a trivial insulator. However, the theorem does not
distinguish between bosonic and fermionic systems. In this work we argue that
in the case of fermionic systems, the topological orders that are compatible
with the microscopic constraints are in general different from the bosonic
case. We find different results in the cases of even and odd denominator
fillings, with even denominator fillings deviating stronger from the bosonic
case. Part of our results also hold in three dimensions.
