Relatively hyperbolic groups with fixed peripherals
We build quasi-isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any finite collection of finitely generated groups H each of which...
| Main Authors: | , |
|---|---|
| 格式: | Journal article |
| 语言: | English |
| 出版: |
Springer
2019
|
| _version_ | 1826304773871108096 |
|---|---|
| author | Cordes, M Hume, DS |
| author_facet | Cordes, M Hume, DS |
| author_sort | Cordes, M |
| collection | OXFORD |
| description | We build quasi-isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any finite collection of finitely generated groups H each of which either has finite stable dimension or is non-relatively hyperbolic, there exist infinitely many quasi-isometry types of one-ended groups which are hyperbolic relative to H. The groups are constructed using classical small cancellation theory over free products. |
| first_indexed | 2024-03-07T06:22:51Z |
| format | Journal article |
| id | oxford-uuid:f34200b2-aa8c-4cb6-b811-4b9b78f0896d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:22:51Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:f34200b2-aa8c-4cb6-b811-4b9b78f0896d2022-03-27T12:10:49ZRelatively hyperbolic groups with fixed peripheralsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f34200b2-aa8c-4cb6-b811-4b9b78f0896dEnglishSymplectic Elements at OxfordSpringer2019Cordes, MHume, DSWe build quasi-isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any finite collection of finitely generated groups H each of which either has finite stable dimension or is non-relatively hyperbolic, there exist infinitely many quasi-isometry types of one-ended groups which are hyperbolic relative to H. The groups are constructed using classical small cancellation theory over free products. |
| spellingShingle | Cordes, M Hume, DS Relatively hyperbolic groups with fixed peripherals |
| title | Relatively hyperbolic groups with fixed peripherals |
| title_full | Relatively hyperbolic groups with fixed peripherals |
| title_fullStr | Relatively hyperbolic groups with fixed peripherals |
| title_full_unstemmed | Relatively hyperbolic groups with fixed peripherals |
| title_short | Relatively hyperbolic groups with fixed peripherals |
| title_sort | relatively hyperbolic groups with fixed peripherals |
| work_keys_str_mv | AT cordesm relativelyhyperbolicgroupswithfixedperipherals AT humeds relativelyhyperbolicgroupswithfixedperipherals |