Codimension one subgroups and boundaries of hyperbolic groups
We construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditch's theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boun...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1797100744662319104 |
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| author | Delzant, T Papasoglu, P |
| author_facet | Delzant, T Papasoglu, P |
| author_sort | Delzant, T |
| collection | OXFORD |
| description | We construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditch's theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boundary can not be extended to splittings over more complicated subgroups. |
| first_indexed | 2024-03-07T05:41:57Z |
| format | Journal article |
| id | oxford-uuid:e5e38b5a-9c02-4fea-8104-1d4c0ee2d4ee |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:41:57Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:e5e38b5a-9c02-4fea-8104-1d4c0ee2d4ee2022-03-27T10:27:09ZCodimension one subgroups and boundaries of hyperbolic groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e5e38b5a-9c02-4fea-8104-1d4c0ee2d4eeEnglishSymplectic Elements at Oxford2008Delzant, TPapasoglu, PWe construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditch's theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boundary can not be extended to splittings over more complicated subgroups. |
| spellingShingle | Delzant, T Papasoglu, P Codimension one subgroups and boundaries of hyperbolic groups |
| title | Codimension one subgroups and boundaries of hyperbolic groups |
| title_full | Codimension one subgroups and boundaries of hyperbolic groups |
| title_fullStr | Codimension one subgroups and boundaries of hyperbolic groups |
| title_full_unstemmed | Codimension one subgroups and boundaries of hyperbolic groups |
| title_short | Codimension one subgroups and boundaries of hyperbolic groups |
| title_sort | codimension one subgroups and boundaries of hyperbolic groups |
| work_keys_str_mv | AT delzantt codimensiononesubgroupsandboundariesofhyperbolicgroups AT papasoglup codimensiononesubgroupsandboundariesofhyperbolicgroups |