We prove that a relatively hyperbolic pair 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.
Cite this article
Bena Tshishiku, Genevieve Walsh, On groups with Bowditch boundary. Groups Geom. Dyn. 14 (2020), no. 3, pp. 791–811DOI 10.4171/GGD/563