Grothendieck's problem for 3-manifold groups

Abstract

The following problem that was posed by Grothendieck: Let u: H → G be a homomorphism of finitely presented residually finite groups for which the extension û: Ĥ → Ĝ is an isomorphism. Is u an isomorphism? The problem was solved in the negative by Bridson and Grunewald who produced many examples of groups G and proper subgroups u: H → G for which û is an isomorphism, but u is not. This paper addresses Grothendieck's problem in the context of 3-manifold groups. © European Mathematical Society.