  We present a perturbative calculation of the neutron matter equation of state
based on low-momentum two- and three-nucleon interactions. Our results are
compared to the model-independent virial equation of state and to variational
calculations, and we provide theoretical error estimates by varying the cutoff
used to regulate nuclear interactions. In addition, we study the dependence of
the BCS $^1$S$_0$ superfluid pairing gap on nuclear interactions and on the
cutoff. The resulting gaps are well constrained by the nucleon-nucleon
scattering phase shifts, and the cutoff dependence is very weak for sharp or
sufficiently narrow smooth regulators with cutoffs $\lm > 1.6 \fmi$.
