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arXiv · 2603.22543

Detecting embedded surfaces using finite quotients

Tam Cheetham-West·Khanh Le
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Abstract

We give conditions on a Haken hyperbolic rational homology three sphere that imply that any other 3-manifold with profinitely equivalent fundamental group must also be Haken. In the appendix, we show that a regular finite-sheeted cover of an aspherical integral homology three-sphere with positive first Betti number must have first Betti number at least four. We also show that this lower bound is sharp.

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Tam Cheetham-West, Khanh Le. 2026-03-23. Detecting embedded surfaces using finite quotients. https://arxiv.org/abs/2603.22543

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