  The large values of the singlet and triplet two-nucleon scattering lengths
locate the nuclear system close to the unitary limit. This particular position
strongly constrains the low-energy observables in the three-nucleon system as
depending on one parameter, the triton binding energy, and introduces
correlations in the low energy sector of light nuclei. Here we analyze the
propagation of these correlations to infinite nuclear matter showing that its
saturation properties, the equation of state of $\beta$-stable nuclear matter
and several properties of neutron stars, as their maximum mass, are well
determined solely by a few number of low-energy quantities of the two- and
three-nucleon systems. In this way we make a direct link between the universal
behavior observed in the low-energy region of few-nucleon systems and
fundamental properties of nuclear matter and neutron stars.
