Cohomology and the Bowditch Boundary

Abstract

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 case of a relatively hyperbolic Poincaré duality group pair, we show 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.

28 pages, 3 figures. This version accepted by Michigan Mathematical Journal. (Reference to GGD in comments on previous version was an error.)