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Bulletin of the London Mathematical Society Advance Access originally published online on April 16, 2008
Bulletin of the London Mathematical Society 2008 40(3):395-404; doi:10.1112/blms/bdn018
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© 2008 London Mathematical Society

Finding relative hyperbolic structures

François Dahmani

Institut de Mathématiques de Toulouse
Université Paul Sabatier
F-31062 Toulouse cedex 9
France

Received 22 September 2006. Revision received 13 July 2007.

We propose an algorithm that recognizes relatively hyperbolic groups from a compatible relative presentation, and even from an arbitrary finite presentation when the parabolic subgroups are abelian. Moreover, it computes important characteristic features such as the hyperbolicity constant of the coned-off Cayley graph. This tool allows us to unify solutions to decision problems for individual groups in the class of relatively hyperbolic groups with abelian parabolics, into a unique solution suitable for every group in the class.

2000 Mathematics Subject Classification 20F67 (primary), 20F10 (secondary).

Partially supported by the ANR (ANR-06-JCJC-0099)


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