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François Dahmani and Asli Yaman
Bounded geometry in relatively hyperbolic groups
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| Published: |
March 21, 2005
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| Keywords: |
Relatively hyperbolic groups, Margulis Lemma, Bounded geometry, asymptotic dimension. |
| Subject: |
20F69 |
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Abstract
If a group is relatively
hyperbolic, the parabolic subgroups are virtually nilpotent if and
only if there exists a hyperbolic space with bounded geometry on
which it acts geometrically finitely.
This provides, via the embedding theorem of M. Bonk and O. Schramm,
a very short proof of the finiteness of asymptotic dimension for such
groups (which is known to imply Novikov conjectures).
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| Acknowledgements
F. Dahmani acknowledges support of the FIM ETH, Zürich.
A. Yaman acknowledges support of the Institute of Mathematics of the University of Bonn and ETH, Zürich. This work was partially done when she was visiting the ETH
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| Author information
François Dahmani:
Labo. E. Picard, Univ. P.Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France.
dahmani@picard.ups-tlse.fr
http://picard.ups-tlse.fr/~dahmani/
Asli Yaman:
IHES Le Bois-Marie, 35, route de Chartres F-91440, Bures-sur-Yvette, France
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