We study quasi-isometry invariants of Gromov hyperbolic spaces, focusing on the lp-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous lp-cohomology, thereby obtaining information about the lp-equivalence\linebreak relation, as well as critical exponents associated with lp-cohomology. As an application, we provide a flexible construction of hyperbolic groups which do not have the Combinatorial Loewner Property, extending [8] and complementing the examples from [10]. Another consequence is the existence of hyperbolic groups with Sierpinski carpet boundary which have conformal dimension arbitrarily close to 1. In particular, we answer questions of Mario Bonk, Juha Heinonen and John Mackay.
Classification :
20-XX
Mots-clés :
Hyperbolic groups and nonpositively curved groups, asymptotic properties of groups, cohomology of groups
Affiliations des auteurs :
Marc Bourdon
1
;
Bruce Kleiner
2
1
Université Lille I, Villeneuve d'Ascq, France
2
Courant Institute of Mathematical Sciences, New York, United States
Marc Bourdon; Bruce Kleiner. Some applications of $\ell_p$-cohomology to boundaries of Gromov hyperbolic spaces. Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 435-478. doi: 10.4171/ggd/318
@article{10_4171_ggd_318,
author = {Marc Bourdon and Bruce Kleiner},
title = {Some applications of $\ell_p$-cohomology to boundaries of {Gromov} hyperbolic spaces},
journal = {Groups, geometry, and dynamics},
pages = {435--478},
year = {2015},
volume = {9},
number = {2},
doi = {10.4171/ggd/318},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/318/}
}
TY - JOUR
AU - Marc Bourdon
AU - Bruce Kleiner
TI - Some applications of $\ell_p$-cohomology to boundaries of Gromov hyperbolic spaces
JO - Groups, geometry, and dynamics
PY - 2015
SP - 435
EP - 478
VL - 9
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/318/
DO - 10.4171/ggd/318
ID - 10_4171_ggd_318
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%J Groups, geometry, and dynamics
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%V 9
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/318/
%R 10.4171/ggd/318
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