On groups with $S^2$ Bowditch boundary

Bena Tshishiku; Genevieve Walsh

doi:10.4171/ggd/563

JournalsggdVol. 14, No. 3pp. 791–811

On groups with $S^{2}$ Bowditch boundary

Bena Tshishiku
Harvard University, Cambridge, USA
Genevieve Walsh
Tufts University, Medford, USA

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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.

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Bena Tshishiku, Genevieve Walsh, On groups with $S^{2}$ Bowditch boundary. Groups Geom. Dyn. 14 (2020), no. 3, pp. 791–811

DOI 10.4171/GGD/563