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

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arxiv 2410.00556 v2 pith:7CXIMJRI submitted 2024-10-01 math.GR math.GT

Henry Wilton , Alessandro Sisto This is my paper · ORCID
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keywords hyperbolicgroupsclasscongruencefinitemappingpropertysubgroup
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Power quotients of surface groups and mapping class groups

    math.GR 2025-07 conditional novelty 8.0 of 10

    For sufficiently large n, the automorphism and outer automorphism groups of the n-power quotient of a hyperbolic surface group are isomorphic to the corresponding power quotients of the extended mapping class group, a...

  2. Regularity of profinite isomorphisms of hyperbolic 3-manifolds

    math.GR 2026-07 accept novelty 6.5 of 10

    Any profinite isomorphism of finite-volume hyperbolic 3-manifolds is regular (μ = ±1) in the sense of Boileau–Friedl.

  3. New tools in hierarchical hyperbolicity: A survey

    math.GR 2025-07 accept

    A survey of tools for hierarchical hyperbolicity, including combinatorial HHSs, injective metrics, asymptotically CAT(0) metrics, curtains, R-cubings, and higher-rank JSJ decompositions.

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