All finitely generated 3-manifold groups are Grothendieck rigid

Abstract

In this paper, we prove that all finitely generated 3-manifold groups are Grothendieck rigid. More precisely, for any finitely generated 3manifold group G and any finitely generated proper subgroup H ă G, we prove that the inclusion induced homomorphism pi : p H Ñ p G on profinite completions is not an isomorphism.