On cohomology of the Higson compactification of hyperbolic spaces

We show that in dimensions $>1$ the cohomology groups of the Higson compactification of the hyperbolic space \H^n with respect to the $C_0$ coarse structure are trivial. Also we prove that the cohomology groups of the Higson compactification of \H^n for the bounded coarse structure are trivial in all even dimensions.