  We present microscopic valence-shell calculations of pairing gaps in the
calcium isotopes, focusing on the role of three-nucleon (3N) forces and
many-body processes. In most cases, we find a reduction in pairing strength
when the leading chiral 3N forces are included, compared to results with
low-momentum two-nucleon (NN) interactions only. This is in agreement with a
recent energy density functional study. At the NN level, calculations that
include particle-particle and hole-hole ladder contributions lead to smaller
pairing gaps compared with experiment. When particle-hole contributions as well
as the normal-ordered one- and two-body parts of 3N forces are consistently
included to third order, we find reasonable agreement with experimental
three-point mass differences. This highlights the important role of 3N forces
and many-body processes for pairing in nuclei. Finally, we relate pairing gaps
to the evolution of nuclear structure in neutron-rich calcium isotopes and
study the predictions for the 2+ excitation energies, in particular for 54Ca.
