  We establish a resonance free strip for codimension 2 symplectic normally
hyperbolic trapped sets with smooth incoming/outgoing tails. An important
application is wave decay on Kerr and Kerr-de Sitter black holes. We recover
the optimal size of the strip and give an $o(h^{-2})$ resolvent bound there. We
next show existence of deeper resonance free strips under the $r$-normal
hyperbolicity assumption and a pinching condition. We also give a lower bound
on the ne-sided cutoff resolvent on the real line.
