On groups with $S^2$ Bowditch boundary

Abstract

We prove that a relatively hyperbolic pair $(G,P)$ has Bowditch boundary a 2-sphere if and only if it is a 3-dimensional Poincare duality pair. We prove this by studying the relationship between the Bowditch and Dahmani boundaries of relatively hyperbolic groups.

Final version that appears in Groups Geom. Dyn. Erratum to the published version attached