On groups with $S^2$ Bowditch boundary

On groups with $S^2$ Bowditch boundary

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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Veröffentlicht in:Groups, geometry and dynamics geometry and dynamics, 2020-01, Vol.14 (3), p.791-811
Hauptverfasser: Tshishiku, Bena, Walsh, Genevieve
Format: Artikel
Sprache:eng
Schlagworte:
Group theory and generalizations
Manifolds and cell complexes
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Zusammenfassung: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.
ISSN:1661-7207
1661-7215
DOI:10.4171/GGD/563