  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
$\mathrm{PSL}(2,\mathbb{Z}[\omega])$ with $\omega^2+\omega+1=0$ is rigid in
this sense. Other examples include the non-uniform lattice of minimal co-volume
in $\mathrm{PSL}(2,\mathbb{C})$ and the fundamental group of the Weeks manifold
(the closed hyperbolic $3$-manifold of minimal volume).

Geometric Topology;Group Theory;Number Theory