Relatively hyperbolic groups: geometry and quasi-isometric invariance
In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for ev...
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| Format: | Journal article |
| Language: | English |
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2006
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| _version_ | 1826272747865505792 |
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| author | Drutu, C |
| author_facet | Drutu, C |
| author_sort | Drutu, C |
| collection | OXFORD |
| description | In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup. |
| first_indexed | 2024-03-06T22:17:29Z |
| format | Journal article |
| id | oxford-uuid:53e2f1e9-07d2-4a01-9949-7eba88bdc9f5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:17:29Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:53e2f1e9-07d2-4a01-9949-7eba88bdc9f52022-03-26T16:34:26ZRelatively hyperbolic groups: geometry and quasi-isometric invarianceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:53e2f1e9-07d2-4a01-9949-7eba88bdc9f5EnglishSymplectic Elements at Oxford2006Drutu, CIn this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup. |
| spellingShingle | Drutu, C Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title | Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title_full | Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title_fullStr | Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title_full_unstemmed | Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title_short | Relatively hyperbolic groups: geometry and quasi-isometric invariance |
| title_sort | relatively hyperbolic groups geometry and quasi isometric invariance |
| work_keys_str_mv | AT drutuc relativelyhyperbolicgroupsgeometryandquasiisometricinvariance |