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Bounded cohomology and isometry groups of hyperbolic spaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hamenstädt, Ursula |
| Copyright Year | 2005 |
| 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. |
| Starting Page | 315 |
| Ending Page | 349 |
| Page Count | 35 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/JEMS/112 |
| Volume Number | 10 |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0507097v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0507097v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0507097v4.pdf |
| Alternate Webpage(s) | http://www.ems-ph.org/journals/show_pdf.php?iss=2&issn=1435-9855&rank=2&vol=10 |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0507097v3.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0507097v4.pdf |
| Alternate Webpage(s) | http://www.math.uni-bonn.de/people/ursula/dyncoho.pdf |
| Alternate Webpage(s) | https://doi.org/10.4171/JEMS%2F112 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
