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

2024/10/01 by Wilton, Henry, Sisto, Alessandro
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.00556

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.

Related

• Determining hyperbolic 3-manifolds by their surfaces
• A congruence subgroup property for symmetric mapping class groups
• 3-manifold groups are virtually residually p
• Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groups
• Commensurability and locally free Kleinian groups