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...
| Päätekijät: | , , , |
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| Aineistotyyppi: | Journal article |
| Kieli: | English |
| Julkaistu: |
Princeton University, Department of Mathematics
2020
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| Yhteenveto: | 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). |
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