Bounded cohomology and isometry groups of hyperbolic spaces

Hamenstädt, Ursula. "Bounded cohomology and isometry groups of hyperbolic spaces." Journal of the European Mathematical Society 010.2 (2008): 315-349. <http://eudml.org/doc/277543>.

@article{Hamenstädt2008,
abstract = {Let $X$ be an arbitrary hyperbolic geodesic metric space and let $\Gamma $ be a countable subgroup of the isometry group $\{\rm Iso\}(X)$ of $X$. We show that if $\Gamma $ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups $H_b^2(\Gamma ,\mathbb \{R\})$, $H_b^2(\Gamma ,\ell ^p(\Gamma ))$$(1< p <\infty )$ are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct product.},
author = {Hamenstädt, Ursula},
journal = {Journal of the European Mathematical Society},
keywords = {bounded cohomology; isometry groups; Bounded cohomology; isometry groups},
language = {eng},
number = {2},
pages = {315-349},
publisher = {European Mathematical Society Publishing House},
title = {Bounded cohomology and isometry groups of hyperbolic spaces},
url = {http://eudml.org/doc/277543},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Hamenstädt, Ursula
TI - Bounded cohomology and isometry groups of hyperbolic spaces
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 315
EP - 349
AB - Let $X$ be an arbitrary hyperbolic geodesic metric space and let $\Gamma $ be a countable subgroup of the isometry group ${\rm Iso}(X)$ of $X$. We show that if $\Gamma $ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups $H_b^2(\Gamma ,\mathbb {R})$, $H_b^2(\Gamma ,\ell ^p(\Gamma ))$$(1< p <\infty )$ are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct product.
LA - eng
KW - bounded cohomology; isometry groups; Bounded cohomology; isometry groups
UR - http://eudml.org/doc/277543
ER -