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Absolute profinite rigidity and hyperbolic geometry

Abstract:
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).
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4007/annals.2020.192.3.1

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Sub department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-0080-9059
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Name:
Royal Society
Grant:
WM110145
Publisher:
Princeton University, Department of Mathematics
Journal:
Annals of Mathematics More from this journal
Volume:
192
Issue:
2020
Pages:
679-719
Publication date:
2020-11-09
Acceptance date:
2020-06-13
DOI:
ISSN:
0003-486X
Language:
English
Keywords:
Pubs id:
1123509
Local pid:
pubs:1123509
Deposit date:
2020-08-04

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