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Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups

Published online by Cambridge University Press:  02 November 2004

FRANÇOIS GAUTERO  and
MARTIN LUSTIG
FRANÇOIS GAUTERO
Affiliation:
Université Blaise Pascal (Clermont-Ferrand II), Campus des Cézeaux, Batiment de Mathématiques, Laboratoire de Mathématiques pures, 63177 Aubière, France. e-mail: francois.gautero@math.univ-bpclermont.fr
MARTIN LUSTIG
Affiliation:
Mathématiques (LATP), Université d'Aix-Marseille III, Av. Escad. Normandie-Niemen, 13397 Marseille 20, France. e-mail: martin.lustig@univ.u-3mrs.fr
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Abstract

We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group with $\integers$, given through an automorphism $\alpha{:}\, G \,{\to}\, G$, is a hyperbolic group relative to certain canonical subgroups of $G$ on which $\alpha$ acts periodically or with linear growth.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 3 , November 2004 , pp. 595 - 611
Copyright
© 2004 Cambridge Philosophical Society

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