  We give a group cohomological description of the \v{C}ech cohomology of the
Bowditch boundary of a relatively hyperbolic group pair, generalizing a result
of Bestvina-Mess about hyperbolic groups. In case of a relatively hyperbolic
Poincar\'e duality group pair, we show the Bowditch boundary is a homology
manifold. For a three-dimensional Poincar\'e duality pair, we recover the
theorem of Tshishiku-Walsh stating that the boundary is homeomorphic to a
two-sphere.
