The congruence subgroup property for mapping class groups and the residual finiteness of hyperbolic groups

Abstract

Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent hyperbolic 3-manifolds are commensurable.

22 pages. Primary article by Wilton, with an appendix by Sisto. v2 incorporates comments on the first version. It includes a more refined profinite-rigidity statement (Theorem B(ii)), proved in the new section 5