On the profinite rigidity of triangle groups
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, that is, each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Wiley
2021
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| _version_ | 1826307903167922176 |
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| author | Bridson, MR McReynolds, DB Reid, AW Spitler, R |
| author_facet | Bridson, MR McReynolds, DB Reid, AW Spitler, R |
| author_sort | Bridson, MR |
| collection | OXFORD |
| description | We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, that is, each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish between the profinite completions of certain groups. |
| first_indexed | 2024-03-07T07:11:33Z |
| format | Journal article |
| id | oxford-uuid:ed02cdab-f815-4ddf-843a-a0b26fc13cc4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:11:33Z |
| publishDate | 2021 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:ed02cdab-f815-4ddf-843a-a0b26fc13cc42022-06-17T09:34:55ZOn the profinite rigidity of triangle groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ed02cdab-f815-4ddf-843a-a0b26fc13cc4EnglishSymplectic ElementsWiley2021Bridson, MRMcReynolds, DBReid, AWSpitler, RWe prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, that is, each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method based on character varieties that can be used to distinguish between the profinite completions of certain groups. |
| spellingShingle | Bridson, MR McReynolds, DB Reid, AW Spitler, R On the profinite rigidity of triangle groups |
| title | On the profinite rigidity of triangle groups |
| title_full | On the profinite rigidity of triangle groups |
| title_fullStr | On the profinite rigidity of triangle groups |
| title_full_unstemmed | On the profinite rigidity of triangle groups |
| title_short | On the profinite rigidity of triangle groups |
| title_sort | on the profinite rigidity of triangle groups |
| work_keys_str_mv | AT bridsonmr ontheprofiniterigidityoftrianglegroups AT mcreynoldsdb ontheprofiniterigidityoftrianglegroups AT reidaw ontheprofiniterigidityoftrianglegroups AT spitlerr ontheprofiniterigidityoftrianglegroups |