We give a group cohomological description of the Čech cohomology of the Bowditch boundary of a relatively hyperbolic group pair, generalizing a result of Bestvina–Mess about hyperbolic groups. In the case of a relatively hyperbolic Poincaré duality group pair, we show that the Bowditch boundary is a homology manifold. For a three-dimensional Poincaré duality pair, we recover the theorem of Tshishiku–Walsh stating that the boundary is homeomorphic to a two-sphere.
"Cohomology and the Bowditch Boundary." Michigan Math. J. 69 (3) 633 - 669, August 2020. https://doi.org/10.1307/mmj/1596700822