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

François Gautero (1) , Martin Lustig (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group G with Z is a hyperbolic group relative to certain canonical subgroups of G on which the automorphism coming from the action of Z on G acts periodically or with linear growth.

Mots clés: mapping-torus; relative hyperbolicity; combination theorem; surface homeomorphism

Domaines: Géométrie métrique [math.MG]

François Gautero, Martin Lustig. Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups. Mathematical Proceedings of the Cambridge Philosophical Society, 2004, 137 (3), pp.595-611. ⟨hal-00808792⟩