  Manifolds with infinite cylindrical ends have continuous spectrum of
increasing multiplicity as energy grows, and in general embedded resonances
(resonances on the real line, embedded in the continuous spectrum) and embedded
eigenvalues can accumulate at infinity. However, we prove that if geodesic
trapping is sufficiently mild, then the number of embedded resonances and
eigenvalues is finite, and moreover the cutoff resolvent is uniformly bounded
at high energies. We obtain as a corollary the existence of resonance free
regions near the continuous spectrum.
  We also obtain improved estimates when the resolvent is cut off away from
part of the trapping, and along the way we prove some resolvent estimates for
repulsive potentials on the half line which may be of independent interest.
