Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groups

Adam Klukowski

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arXiv · 2411.06867

Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groups

Adam Klukowski

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Abstract

We prove the Congruence Subgroup Property for two families of subgroups of Mapping Class Groups of finite-type surfaces. The first one is related to nilpotent quotients of the fundamental group and Johnson filtration, and along the way we give an elementary proof of a theorem of Ben-Ezra-Lubotzky. The second family consists of certain geometric subgroups obtained via subsurface inclusions.

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Adam Klukowski. 2024-11-11. Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groups. https://arxiv.org/abs/2411.06867

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