Absolute profinite rigidity and hyperbolic geometry
We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group PSL(2, Z[ω]) with ω2 + ω + 1 = 0 is rigid in this sense. Other examples includ...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Princeton University, Department of Mathematics
2020
|
| _version_ | 1826305670028197888 |
|---|---|
| author | Bridson, M McReynolds, DB Reid, AW Spitler, R |
| author_facet | Bridson, M McReynolds, DB Reid, AW Spitler, R |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group PSL(2, Z[ω]) with ω2 + ω + 1 = 0 is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in PSL(2, C) and the fundamental group of the Weeks manifold (the closed hyperbolic 3–manifold of minimal volume). |
| first_indexed | 2024-03-07T06:36:21Z |
| format | Journal article |
| id | oxford-uuid:f7c8ebc9-a90b-4222-981b-fbec3464c0ec |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:36:21Z |
| publishDate | 2020 |
| publisher | Princeton University, Department of Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:f7c8ebc9-a90b-4222-981b-fbec3464c0ec2022-03-27T12:45:12ZAbsolute profinite rigidity and hyperbolic geometryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f7c8ebc9-a90b-4222-981b-fbec3464c0ecEnglishSymplectic ElementsPrinceton University, Department of Mathematics2020Bridson, MMcReynolds, DBReid, AWSpitler, RWe construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group PSL(2, Z[ω]) with ω2 + ω + 1 = 0 is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in PSL(2, C) and the fundamental group of the Weeks manifold (the closed hyperbolic 3–manifold of minimal volume). |
| spellingShingle | Bridson, M McReynolds, DB Reid, AW Spitler, R Absolute profinite rigidity and hyperbolic geometry |
| title | Absolute profinite rigidity and hyperbolic geometry |
| title_full | Absolute profinite rigidity and hyperbolic geometry |
| title_fullStr | Absolute profinite rigidity and hyperbolic geometry |
| title_full_unstemmed | Absolute profinite rigidity and hyperbolic geometry |
| title_short | Absolute profinite rigidity and hyperbolic geometry |
| title_sort | absolute profinite rigidity and hyperbolic geometry |
| work_keys_str_mv | AT bridsonm absoluteprofiniterigidityandhyperbolicgeometry AT mcreynoldsdb absoluteprofiniterigidityandhyperbolicgeometry AT reidaw absoluteprofiniterigidityandhyperbolicgeometry AT spitlerr absoluteprofiniterigidityandhyperbolicgeometry |