Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 3, pages 51-97.

Boundaries of strongly accessible hyperbolic groups

B H Bowditch

Abstract. We consider splittings of groups over finite and two-ended subgroups. We study the combinatorics of such splittings using generalisations of Whitehead graphs. In the case of hyperbolic groups, we relate this to the topology of the boundary. In particular, we give a proof that the boundary of a one-ended strongly accessible hyperbolic group has no global cut point.

Keywords. Boundary, accessibility, hyperbolic group, cutpoint, Whitehead graph

AMS subject classification. Primary: 20F32.

E-print: arXiv:math.GR/9810187

Submitted: 15 November 1997. (Revised: 10 August 1998.) Published: 25 October 1998.

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B H Bowditch
Faculty of Mathematical Studies, University of Southampton
Highfield, Southampton SO17 1BJ, Great Britain
Email: bhb@maths.soton.ac.uk

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