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. 
Alexander Dranishnikov and Thanos Gentimis
math.AT