All finitely generated 3-manifold groups are Grothendieck rigid

Hongbin Sun

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arXiv · 2103.00547

All finitely generated 3-manifold groups are Grothendieck rigid

Hongbin Sun

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Abstract

In this paper, we prove that all finitely generated 3-manifold groups are Grothendieck rigid. More precisely, for any finitely generated 3-manifold group $G$ and any finitely generated proper subgroup $H<G$, we prove that the inclusion induced homomorphism $\widehat{i}:\widehat{H}\to \widehat{G}$ on profinite completions is not an isomorphism.

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Hongbin Sun. 2021-02-28. All finitely generated 3-manifold groups are Grothendieck rigid. https://arxiv.org/abs/2103.00547

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