Absolute profinite rigidity and hyperbolic geometry

Martin R. Bridson

doi:10.4007/annals.2020.192.3.1

Absolute profinite rigidity and hyperbolic geometry

2020-11-01

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DOI：10.4007/annals.2020.192.3.1

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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[omega]) with omega(2) + omega + 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).

Keywords:

Profinite completion

rigidity

hyperbolic 3-orbifold

hyperbolic 3-manifold

Bianchi group

Weeks manifold

Absolute profinite rigidity and hyperbolic geometry

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