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arXiv · 2410.00556

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

Henry Wilton·Alessandro Sisto
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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.

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Henry Wilton, Alessandro Sisto. 2024-10-01. The congruence subgroup property for mapping class groups and the residual finiteness of hyperbolic groups. https://arxiv.org/abs/2410.00556

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