All finitely generated 3-manifold groups are Grothendieck rigid (Q6039648)

Summary: 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 show that the inclusion induced homomorphism \(\widehat{i} : \widehat{H} \to \widehat{G}\) on profinite completions is not an isomorphism.