# Bounded cohomology and isometry groups of hyperbolic spaces

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 2, page 315-349
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topHamenstädt, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.